Try saving up until you have about $800 or so.
Contrary to what most people in here are saying, you don't need i7. The difference between i7 and i5 is negligible. Just get this as an i5.
Newegg.com - Intel Core i5-2500K Sandy Bridge 3.3GHz (3.7GHz Turbo Boost) LGA 1155 95W Quad-Core Desktop Processor Intel HD Graphics 3000 BX80623I52500K
If you're on a tight budget, this is probably a pretty solid video card for you:
Newegg.com - HIS H675F1GD Radeon HD 6750 1GB 128-bit GDDR5 PCI Express 2.1 x16 HDCP Ready CrossFireX Support Video Card with Eyefinity
This case is pretty legit as far as air efficiency and price goes:
Newegg.com - Antec Three Hundred Illusion Black Steel ATX Mid Tower Computer Case
We're already up to 380. Add in the power supply at around 600-700Wattage of power and we're around $500. You can then get a motherboard and 8GB of DDR3 for around 200-250ish. You can take your old hard drive and optic drive (CD-ROM/DVD/Blu-Ray player) and throw it in this machine to complete it.
$800 is about right for setting yourself up for a nice beast-mode gaming PC that will be straight for AT LEAST the next couple of years. Worst case scenario, you make a small $100-150 investment down the road to upgrade your video card and maybe add more RAM.
Honestly though, $500 is getting to the point where you're gaming on a PC that's already bottlenecked by it's hardware and struggling to run a lot of current games at Medium settings. If you wait til you got about $700-800, you can run a lot of games now on High, no sweat, and you can continue to not have to worry about falling behind for at least another calendar year.
Hope this helps man. PM me if you need some more info.
Edit: If you're looking for a pre-built machine, sorry man. I've always just built PCs and I'm not very knowledgable regarding the current market for price and capability of current desktops for gaming.