$500 won't go terribly far for a gaming PC, but you can definitely get something that'll run them at moderate settings.
Even though you say you're "computer illiterate" I'd highly recommend building it yourself, as it's no more difficult then assembling a Lego kit and your gaming dollar will go much farther. If you want to hop on FAF chat, look for myself, Viking, MagicDoc or ToejamS and we'll be glad to help you nail down the exact parts based on what you need. Here's an example build:
Motherboard:
http://www.newegg.com/Product/Product.a ... 6813130653CPU:
http://www.newegg.com/Product/Product.a ... &Tpk=2500kRAM:
http://www.newegg.com/Product/Product.a ... 6820233186PSU:
http://www.newegg.com/Product/Product.a ... 6817139027Case:
http://www.newegg.com/Product/Product.a ... 6811815014Depending on how flexible your budget is, you could either use the 2500k's integrated graphics or add a dedicated GPU. You could also reuse parts from your current machine such as your hard drive and optical drive to save more and put it into better hardware.
If you're strongly against building it yourself, then you're pretty much at the mercy of whatever brand-name box you can find - for example, this seems decent:
http://www.newegg.com/Product/Product.a ... 6883229285