You generally can upgrade to a low end gaming system for about $320-380, assuming you don't need a new case, PSU, optical drive, etc. that will play most games at playable framerates at low to modeate settings:
CPU - low end dual core or cheap quad $100
Mobo for single card $70-100
Memory - 4 GB $80-100
Graphics card $60-80
When upgrading though, the old PSU most likely is to small and replacing it will add another $50-80. If you find good sales or the right combo deals , you might be able to knock $20-40 off the total above.
The above assumes a low end gaming card - for another $20-30 you can take a major step up in frame rates - but still at the upper mainstream level, not the enthusiast level.
To go higher you need to upgrade the CPU as well as the graphics card.
The link below shows you approximately what you can expect in that budget range using a 4670 video card. Note that the benchmarks were made using a system designed so the rest of the system would not constrain the graphics card - most importantly a fast CPU. While the CPU in this budget range should mostly keep up with a 4670 - some results may be a little lower - but on the whole decent low end game play.
http://www.tomshardware.com/charts/gaming-graphics-cards-charts-q3-2009-mainstream-quality/compare,1374.html?prod%5B2594%5D=on
Its pretty hard to go much lower in price without one thing or another affecting play, or low quality components.