Are you comfortable with building a computer yourself? If so, here is are some specs that will give you the most power for your budget. Monitor, keyboard, and mouse are not included. Items are from Newegg unless otherwise noted and include all rebates, discounts, and promos that apply. Prices are rounded.
AMD FX-6100 3.3GHz AM3+ 95W Six-Core Processor ($120) ASUS M5A78L-M LX PLUS AM3+ Micro ATX Motherboard ($45) or ASUS M5A78L-M LX3 Motherboard - AMD 760G Chipset (Also $45) ASUS HD7850-DC-1GD5 Radeon HD 7850 1GB 256-Bit ($125) ASUS DVD-Writer Black SATA Model DRW-24F1ST Drive ($16) Western Digital Caviar Blue 1TB 7200 RPM 64MB Hard Drive ($55) COOLMAX ZX Series ZX-700 80-Plus Certified 700W PSU ($30) Crucial Ballistix 4GB 240-Pin DDR3 DDR3 1600 Ram ($35)
Plus 2 Free games.
$425 -10% off entire newegg purchase promo code $382.50 Plus Microsoft Windows 7 Home Premium SP1 64-Bit ($75, from DMS, eBay, etc) $457.50
You can spend up to $46.75 on a case of your choice (plus fans- don't forget) if you buy from Newegg (The 10% off will bring the $46.75 down to $42.50 for a total of $500).
Feel free to make changes . Let me know if you have any questions.