Any advice on reducing front panel jack noise?

If you use the jacks the other way around (headphones to the front panel, speakers to the rear jack), does it make any difference ?

Well, the problem is definitely caused by the front panel then, and the simplest solution is not using the front panel. It is often badly implemented in PCs, and is prone to interference due to ground loops and/or EMI. It can be fixed or improved by DIY modifications, but this is only recommended if you are familiar with making such changes. A different case could also fix the problem, but it is a rather inconvenient solution, and the new case might be just as bad anyway.

So, without using the front panel, some possible solutions include:

- connecting either the headphones or the speakers to the front channel jack at the rear; this is cumbersome due to the constant unplugging

- doing the same with a simple external switchbox to avoid having to unplug the other device

- a splitter and a cheap (e.g. FiiO) headphone amplifier on the rear jack

- using a cheap external DAC for the speakers, like the FiiO D3 that can be connected to the S/PDIF output of the sound card

- connecting the speakers to the rear (surround) channels, and using stereo upmixing to 4 channels; unfortunately, this solution would probably only work with some software, and not others (depending on what Windows audio API they use)

I cannot recommend a particular brand, but if the switchbox is reasonably good (it does not have to be expensive), it should not audibly degrade the sound.

Try searching for a suitable device here, for example. This one seems to do what you are looking for, although it costs almost as much as a FiiO D3, and also has a microphone input/output, which is unneeded.

It is also possible that you have damaged the front panel 1/8" socket in some way. 

This is easily done i.e by brushing past it or standing up suddenly when wearing headphones. This is one reason why pro grade gear uses XLR  or 1/4" jacks and sockets.

Replacing the original socket might be a fiddly job so an inexpensive solution would to add a new set of sockets via something like http://www.scan.co.uk/products/silverstone-sst-fp32s-35-front-i-o-module-in-silver

Open up your PC and trace back the audio connection wires to where they terminate on a set of pins on the motherboard. Disconnect and reconnect the new leads. If in doubt dig out the manual for full details.

STV makes a good suggestion re a splitter box. He says himself he cannot recommend brands so I hope he doesn't mind me mentioning that I got one of those devices he links to from Maplins ages ago and it didn't last very long before it started spitting and crackling. Might just have been a bad example.

A more permanent, if more costly, solution would be to get one of the new breed of inexpensive pro-am audio USB audio interfaces. This will have better quality sockets, Probably 1/4" jack.

I also own an Antec case and had the same kind of specific problem. Does the buzzing varies with what you are doing, for example when the display changes?

Then it's a ground loop problem. I had that problem on the Antec 900. The only real solution for front panel was to cut useless wires in it, which I can't do on mine without destroying the case.

My tradeoff: unscrew and isolate the black cable going from the front panel to the chassis, and unplug the USB and Firewire from the motherboard. It's inconvenient as you lose the front USBs, but you can always go back (nothing cut), and it can be worth it if you frequently plug/unplug your headphones. I had huge buzzing problems (it was unusable at high volume), and I get absolutely none after the fix :)

You can always use a USB extension cord and/or hub, but then you're nearly back to the same kind of things as suggested above (except it's time it's usb, not audio). That's what I do at the moment.

I was as disappointed as you when I found out that it came from my case. I spent quite a while trying to find the cause, thinking it was either the sound card or interferences... in the end it's just stupidly bad case design.