$200-400 computer that will run it??? Very hard to find.
On that budget, you don't need a quad core to run games. Most duo cores are still fine. The i3's have 4 threads anyway i think (not sure, they should) which is like a virtual quad-core.
If you can pay a little more newegg has an amazing bundle deal right now.
http://www.newegg.com/Product/ComboB...t=Combo.558462
Thats a pretty amazing setup for the price.
Otherwise, this build i put together is better if you can use ur old hard drive
HAF 912
HIS 5770
Antec Earthwatts 650w
G.Skill Ripjaws 4GB DDR3
Biostar T5 XE CFX-SLI
Intel i3-550
Total price is $520 after rebate and $550 before. They all have free shipping.