Need some budget speakers with LOTS of bass!

I had the logitech z2300, yes there very loud with loads of bass, but the quality of the sound is quite awful , it sounds like it's only playing 1 note of bass the whole time, the sub sounds confused and muddy, the satilites have no mid-range, also if played at loud volumes they start to over heat very quickly and you can smell them burning, a good alternative is the edifier s530 or s730 will be just as loud and have alot of bass impact but way better sound quality and they won't overheat.

Are you up to buying used, and perhaps floorstanding speakers?

A pair of used Cerwin Vegas or old Infinity SM-series speakers would suit you perfectly when paired with a cheap amp.

Okay, well that's fine.  What I would do - and that's because I'm concerned about sound quality and more than one-note flabby bass - is get this bookshelf speaker/amp bundle (I have it, it's great!) and one of these subwoofers:

http://www.parts-express.com/pe/showdetl.cfm?Partnumber=300-633
http://www.parts-express.com/pe/showdetl.cfm?Partnumber=303-430

http://www.parts-express.com/pe/showdetl.cfm?Partnumber=309-177

http://www.parts-express.com/pe/showdetl.cfm?Partnumber=309-177

These will outperform any marketed "multimedia" speakers in every imaginable way, including quantity and (above all) quality of bass.  There's a reason you don't see specs marketed for multimedia speakers...

You'll need RCA interconnects to go to the sub from your sound card/DAC to the sub and from the sub to the amp; and speaker wires too.  That's another $5-$10, so you're looking at a little over $200 total - not much for the superb quality of sound you get.

You're not going to reach party level SPL with PC speakers. For one they are not big enough and their "subwoofer" is more like a fart machine mixed in with some distortion. Cranking them is more embarrassing than anything else. If you want volume/bass then you should really consider a bookshelves/subwoofer combo like suggested by BlackbeardBen. Even then though, the amount of bass you are going to get out of any setup also depend on the size of the room that they are in. You could get a Bic F-12 sub for less than $200 off of Ebay. That would certainly get you the bass you want.