It’s a little tricky to get any decent computer gaming or otherwise for that low a price. Note that the $300 rig @jaytkay linked to listed a price of $0.00 for Windows? That right there means that you will pay more than $300 for that rig unless you already have a legal retail copy of Windows that you can install. And the Maximum PC $500 build has a similar omission: “In order to keep the machine under $500, we factored out the price of purchasing an operating system, and assume that you already have a copy of Windows XP, Vista, or the Windows 7 Beta lying around.”
At that price point, you will be building your own, and you must already have an operating system to install.
I managed to shop around and got a Core i3 with 6GB RAM, a 1TB drive, and Win7 Home Premium for $500. I am sure that with a little shopping, you could find something comparable and a graphics card to cover that one relative weak spot if you need more oomph. Then again, the Core i3’s integrated graphics are about on par with the Radeon 9800 GT I had in my old rig not “kick ass” but it gets the job done. I only made it choke on one game so far which should be enough to hold you over until you can save up for a card.
Still, at $400, you won’t get much, and likely not even get Windows. Bring it up to $500 or have a “free to you” OS like a retail (non-OEM) copy of Windows and your options increase exponentially.
.
@filmfann @wenn To each their own, but I think that the OP has already chosen a platform.