[MajorError]

  If you're not gaming you can build a computer for super cheap. Lower that budget to around $750, get a nice looking case (something aluminum or from Corsair), get an i3/APU for CPU, proper motherboard with the connections you need, reliable 450W power supply (i.e. Antec earthwatts), small 64GB SSD for booting, and lots of storage hard drives, which is dirt cheap (last storage HDD sale was two days ago, $100 for 3TB Toshiba drive) and you should be good to go. Spend the extra money on a new pair of phones or something. 

There's also the ultimate in compactness:  the Intel NUC http://www.intel.com/content/www/us/en/nuc/overview.html
~$650 on Newegg will get you an i5 model, 16Gb RAM, and a 120Gb mSATA drive.  another $34 would add wireless capability

 

[ohhgourami]

I think the Gigabyte Brix is better than the NUC.

 

[MajorError]

I think the Gigabyte Brix is better than the NUC.

Certainly if you went for the i7 model, but that's almost $800 just to get started.
The whole point of my suggestion was to illustrate that one could get mainstream processing power (i5) in a very small form-factor for under $700, as opposed to the previously suggested entry-level system (i3).  The other nice thing about the i5 NUC is that it has 3 video outputs (1xHDMI, 2xDP) whereas the i5 Brix only has a single HDMI, and the poster that the suggestion was meant for stated a multiple display capability.
 
The biggest frustration in dealing with a NUC is that Intel doesn't include the AC side of the power adapter like this one.

 

[MooTaters]

   
 
You can build this machine for considerably less.  Now if you are into gaming, then I'd say your budget is about right.  But for basic use, media, with dual monitors you don't need to spend that much.
Liquid cooling is not more quiet. LC uses radiators that have fans.  A good (read that "large") case with air cooling is extremely quiet. The key is large, slow spinning fans, which you typically find on full-towers...not so much mid-towers (but there are exceptions)
The only people that "need" liquid cooling are hardcore overclockers who want to milk every smidgeon of performance from a machine.   A well thought out air-cooled PC will be just as quiet for a lot less money, just pay attention to what case you get.   I'm not a fan of the test bench builds, simply because I want all my expensive components secured in the relative protection of a case.
 
I personally wouldn't bother with a in-board sound card and go with an external DAC.  This opens up way more options.   Some of today's portable DAC/amps are very good and let you take your act on the road with a portable source (phone) and IEMs. 

 
I wouldn't call the 600t quiet.  It does have large fans, but definitely not quiet, and though it's a midtower most would agree when I say it barely fits into that form factor.  That said in awsanderson's case leaving the fans on low using the built in fan controller would help.  Part of the problem is, as far as I've noticed, I'm pretty sure over time the 600t's fans really increase in volume(when first turning it on they're pretty quiet).  I'd argue something like the Fractal Define R4 would help for a silent PC much more than 600T...being that's the main idea behind it's design.  That said all that extra noise dampening material does add weight, but as long as it's not moving often that shouldn't be a problem.  Corsair also has some decent offerings in the area of silent cases(330R, and 550D).
 
A lot of noise is created through sound reverberating off panels inside cases, so noise-damping built in on cases will help.  Also most case manufacturers include rather cheap fans so fan upgrades help, and if you notice the front of silent cases always have a front door which has noise dampening because a good chunk of noise comes from intake fans(which are usually the nearest fan to the person, but not always the case).  Another little note on noise, a lot of what causes fan noise is anything in the way of airflow.  An example being many 600T owners out there that aren't afraid of losing their warranty have found some pretty decent improvements by cutting away the mesh grill on the front intake fan(not the part with the built in fan filter that you see on the outside).  Keeping dust at bay also helps, so if you can keep your computer elevated at least a foot off the floor if you can.
 
EDIT: Though I know users here are just as knowledgeable, checking out communities like the ones on the linustechtips forums or teksyndicate forums can also help.   Always make sure though to post what you're building for(gaming, silent, etc.) of course so people can give accurate suggestions.

 

[MajorError]

   
A lot of noise is created through sound reverberating off panels inside cases, so noise-damping built in on cases will help.  Also most case manufacturers include rather cheap fans so fan upgrades help, and if you notice the front of silent cases always have a front door which has noise dampening because a good chunk of noise comes from intake fans(which are usually the nearest fan to the person, but not always the case).  Another little note on noise, a lot of what causes fan noise is anything in the way of airflow.  An example being many 600T owners out there that aren't afraid of losing their warranty have found some pretty decent improvements by cutting away the mesh grill on the front intake fan(not the part with the built in fan filter that you see on the outside).  Keeping dust at bay also helps, so if you can keep your computer elevated at least a foot off the floor if you can.

 
There's also the corner-case of a multi-GPU/card gaming system, and the one fan you have considerably less control over:  the PSU fan.
 
Until I built my Ivy-Bridge i5 system, I never really had a noise issue.  I had a single 570 GTX in the prior Q6600 system on a 500w PSU, and even under load, the most-annoying fan was the northbridge cooler.  The case fans on the i5 setup are low-noise Noctua fans, and I never hear them.  The reference blowers on the pair of 570s even at maximum are comparatively quieter and much less annoying than the single 120mm PSU fan under modest load.  It's the one thing I overlooked on this first-time SLI build...
 
I'd suggest looking at QuietPC.com for reputable "quiet supplies"

 

[MooTaters]

   
There's also the corner-case of a multi-GPU/card gaming system, and the one fan you have considerably less control over:  the PSU fan.
 
Until I built my Ivy-Bridge i5 system, I never really had a noise issue.  I had a single 570 GTX in the prior Q6600 system on a 500w PSU, and even under load, the most-annoying fan was the northbridge cooler.  The case fans on the i5 setup are low-noise Noctua fans, and I never hear them.  The reference blowers on the pair of 570s even at maximum are comparatively quieter and much less annoying than the single 120mm PSU fan under modest load.  It's the one thing I overlooked on this first-time SLI build...
 
I'd suggest looking at QuietPC.com for reputable "quiet supplies"

 
 
That is true, GPU's get excessively loud if you don't use something like EVGA precision x to create a fan curve that doesn't allow it to get too loud.  Or buy one with an aftermarket cooler, even if GTX780/Titan stock coolers look great.  Also would say with reference to the PSU fan, as long as you don't buy the cheapest thing on the market you're probably fine(unless you're never under serious load).  That said I still have yet to upgrade from my old 680w thermaltake PSU that has I'm guessing 2 90mm fans on it(haven't measured, but they don't get loud), yes it's that old.  I have heard some good things about corsair's new silent series PSU's(which go beyond picking a quiet fan and fan curve), and I'm sure the ability to have the fan intake from the bottom might help(purely speculation though).

 

[MajorError]

   
 
Also would say with reference to the PSU fan, as long as you don't buy the cheapest thing on the market you're probably fine(unless you're never under serious load).

Even with quality components, it becomes a matter of how much power is being drawn through the system.  I've used a variety of Seasonic PSUs from 350w through the current 850w which is louder by at least an order of magnitude.  Even 80+ Platinum-certified PSUs are going to get loud under load, it's just a matter of how much longer it takes for them to get there.
 
Suffice to say, you can build a dead-silent, fanless general-purpose system, or you can build a gaming system--as you add performance, the noise floor will rise in lock-step.

 

[ohhgourami]

  Certainly if you went for the i7 model, but that's almost $800 just to get started.
The whole point of my suggestion was to illustrate that one could get mainstream processing power (i5) in a very small form-factor for under $700, as opposed to the previously suggested entry-level system (i3).  The other nice thing about the i5 NUC is that it has 3 video outputs (1xHDMI, 2xDP) whereas the i5 Brix only has a single HDMI, and the poster that the suggestion was meant for stated a multiple display capability.
 
The biggest frustration in dealing with a NUC is that Intel doesn't include the AC side of the power adapter like this one.

That was a bit lazy on my part. I picked the Brix since I know it runs passively, while forgetting only having 1 video out. If I remember correctly, the first gen NUC had a fan.
 
If all he needs his PC is to browse and play music, then even an i3 would suffice. The key here is to use passive cooling. If the NUC is pure passive cooling, that would be the pre-built of choice. Especially with a 2k budget, he can pack a 500gb mSATA ssd for it.
 
If I had to build this myself, I'd probably work around this case: http://www.silentpcreview.com/Akasa_Euler_Fanless_Thin_ITX_Case

 

[MooTaters]

  Even with quality components, it becomes a matter of how much power is being drawn through the system.  I've used a variety of Seasonic PSUs from 350w through the current 850w which is louder by at least an order of magnitude.  Even 80+ Platinum-certified PSUs are going to get loud under load, it's just a matter of how much longer it takes for them to get there.
 
Suffice to say, you can build a dead-silent, fanless general-purpose system, or you can build a gaming system--as you add performance, the noise floor will rise in lock-step.

There was a reason I mentioned the new corsair RM series of PSU's.  They don't just choose a quiet fan/fan curve, they pick out components specifically to get rid of humming, coil whine, and issues of that sort.  It really surprises me though that PSU's today unless they are the cheapest of the cheap would create that much noise when mine is inaudible over all my other components.  And the Platinum cert would only apply to components and energy efficiency of them, it doesn't mean they have to make it quiet. 
 
Like you said though you can use sites like QuietPC, and many other sites out there that review these products beyond what most of us would do to allow us to make better decisions.  I know HardwareSecrets.com has done some pretty extensive reviews of power supplies and many other products.
 
Here's an unboxing/overview of the RM850:

 

[MajorError]

 
There was a reason I mentioned the new corsair RM series of PSU's.  They don't just choose a quiet fan/fan curve, they pick out components specifically to get rid of humming, coil whine, and issues of that sort.  It really surprises me though that PSU's today unless they are the cheapest of the cheap would create that much noise when mine is inaudible over all my other components.  And the Platinum cert would only apply to components and energy efficiency of them, it doesn't mean they have to make it quiet. 

Energy efficiency is still relevant to the noise discussion since it's a measure of how much input is lost to heat.  A low-efficiency PSU will ramp up its fan sooner and faster than one of higher efficiency.

 

[awsanderson]

Thanks for all the info, although some of it went right over my head

.  I already have a stand alone DAC, a Schiit Gungnir, so can I completely skip a sound card or will I still need one, ie, without a sound card when I try to play a song what sends the info to the dac? <-----probably a noob question
My current computer "skips" while loading some web pages and I'm told that more RAM should help with that, I was thinking around 8-16 although I don't want to get too high and cause the PSU to be louder, if that is even a real problem I don't know...   I don't do any gaming so I don't think I need something with too much RAM but is more better?   I want to build something that will last me a long time.
 
Any recommended disc drives?  hard drives?  other components I've never heard of?

 

[awsanderson]

liquid cooling is probably out my current computer is an all in one and I have almost no noise problems, I guess I'll just need to avoid noisy components.
 
again thanks for the info
 
and the tolerance

 

[ohhgourami]

  Thanks for all the info, although some of it went right over my head

.  I already have a stand alone DAC, a Schiit Gungnir, so can I completely skip a sound card or will I still need one, ie, without a sound card when I try to play a song what sends the info to the dac? <-----probably a noob question
My current computer "skips" while loading some web pages and I'm told that more RAM should help with that, I was thinking around 8-16 although I don't want to get too high and cause the PSU to be louder, if that is even a real problem I don't know...   I don't do any gaming so I don't think I need something with too much RAM but is more better?   I want to build something that will last me a long time.
 
Any recommended disc drives?  hard drives?  other components I've never heard of?

No soundcard needed unless you need surround sound for videos.
 
Skips/dropout sounds like a CPU limitation or jitter. You should be perfectly fine with a modern i3. Even 4gb ram would be sufficient even for most gaming so 4gb is more than enough for browsing and music. If you go with the NUC, you will need to get a power brick which runs passive so no noise there. Do you really need a disc drive? IMO, disc drives are obsolete as almost everything can be downloaded, but I can see why you might need if you play CDs. If you need the build to be as quiet as possible, SSDs are definitely the way to go. A big plus is everything feels extremely snappy!

 

[Sniping]

Yeah, restating above memory is no longer a limitation in computers and 4GB will be enough for you, anything more for what you do is simply a waste. As for the hard drives, you should just keep an eye out for the cheapest ones, don't worry about the speeds, hard drives are meant to be mass storage devices. Use a small SSD for speed. There was a 3TB Toshiba drive on sale like two days ago for $100...you should be looking for deals like those and just ordering 2 or maybe even 3 of those drives depending on how much of a storage fiend you are with your music. 

 

[awsanderson]

No surround sound, only two channel.
I do have some cd's and a disc drive but if nothing else I can just import them to my current pc move them to a external hard drive then move them to the new computer.  I rarely get new CD's
I just looked my current PC has 450 gigs and says 229 are free...  I move stuff I rarely use to my external hard drive so storage should not be a problem
will the mother board have the outputs I want?  If I don't use a sound card or a disc drive where will my audio and video outs come from?