Um... are you looking for perhaps a SFF or barebones?
If you are not looking for one of those, then you should consider moving this to the general hardware forum perhaps...
However, for $350 you really are not going to be able to find anything that is decent for gaming. Decent for word processing and web surfing perhaps... but not gaming. I mean come one, a truly decent graphics card will run you at least $100. Plus you will need at least a gig of ram and that is another $100 or so. and call it maybe $100 or so for an almost decent cpu mobo combo. PLus the hard drive, plus teh case, plus the power supply. See the problem with this scenario is that even if you were to get the decent mobo/cpu/ram... it probably will not include the vid card, it is more likely that it will only have an onboard graphics chip.
So, it is highly unlikely that you will be able to score a decent gaming rig for $350 or less.