I have a Radeon HD 2600 XT and I was wondering if there was a way I could hook up my 360 via Component cables to my graphics card, then hook my up monitor to that same graphics card and display my 360 on the monitor?

That card, as almost all video cards, does not have a video input...only outputs.

Besides, that's adding an unnecessary step. You can simply hook up the cables directly to the monitor (granted that requires you to unhook something else).

Video cards are only designed for output, therefore that is all they can do. You are better off (like Viper said) to hook the console directly to the monitor. You may have to get a converter box to do this.

There are cards that do video capture.

Yours is not one of them.

Your best bet would be to hook it up directly to the monitor, assuming you have the correct cables/adapters to do so. If you don't have the cables/adapters then I highly recommend you shop at monoprice.com to get them.

There was this Radeon line, the All-in-Wonder that had inputs too. No idea if they are produced anymore.

Yours doesn't has inputs like everyone said.

You can get a cable to plug an Xbox 360 into VGA.

http://ati.amd.com/products/aiwhd/specs.html