ok, I'm still confused a bit so let me try to lay it out.
you have 1 tv that you're using to as a pc monitor and as a screen for your xbox360. Both pc and xbox are connected to the tv via different input ports. I think we are ok up till here.
you have a video capture card that is connected to computer, I guess? if not, can you tell me what make/model capture card you got so we can be on common ground?
if you got the capture card in your computer, how are you connecting the xbox to the capture card?
the tv cannot pipe the signal from 1 peripheral to another.
typically you will have the capture card connected directly to the xbox for input.
If I'm missing some piece of information, please let me know.