So I was pritty much wondering if I took the composite cable from my 360 and plugged it into the composite ports on my computer shown here:

http://hardwarelogic.com/articles/Mi.../HP_OEM_A2.jpg

If it would work, thanks

As a VIDEO source, yes it would.

So how do I get it to play the 360?

That's up to you. The composite port on your computer is useless unless you've installed some sort of video control software. It should already be there if the port was on your computer to start.

You need to find that software and activate it, tell it to display the Video channel on your screen full-screen. Then play your game.

Do you know of any good video software I could download?

What's the model of your HP? Is this a Media Edition computer?
How long ago did you buy it?