Decent gaming computer for $750 to $800?

I'm thinking about building a computer (it would be my first), and I want it to be able to handle some modern games at decent settings (dead space, bioshock, COD4, maybe sims 3...) Would it be possible to put together a computer that's capable of this for $800 or less, including monitor? I know that's probably pushing it. If anyone could help me out by recommending a build or some parts, I'd appreciate it a lot. Thanks