Actually, you can get hardware that doesn't even need a PC on to work. Viewsonic makes something that will connect between your PC and monitor, and will also accept incoming connections from other video sources and has a TV tuner, too. This one lists for $200.

Fullscreen video and audio combined will almost certainly not be available over the USB bus, since it only recently expanded with enough bandwidth to handle video.

Does the x-box have s-video out? That will open up many options that standard RCA video cables won't. To connect audio, you could also avoid the PC and connect the red and white cables directly into your PC speakers with a simple RCA to mini adapter.