You didn't answer his question.
Liam is assbackward good at building PC's, but he can't work miracles. It's damn near impossible to get a decent gaming computer for $500. Tha't the one caveat of building a computer, even though you can get waaay more bang for your buck, you still need to spend about the same.
Actually, I did. For about under $500 I got a Core 2 Duo E7300 2.66 GHz, a 400w Corsair power supply, a good motherboard, some RAM and a GeForce 9800GT. Yes, under $500. I re-used my case, DVD drive, hard drive, monitor, speakers and keyboard but over the past 9 months I got new speakers, keyboard and monitor.
TL;DR if you're on a tight budget just use any old stuff you can.