Capture from composite video is not really a problem...but what you are talking about is capture from a VGA (or even DVI) output. Not only do you need a capture device that has VGA/DVI input, you need something that can handle potentially massive resolutions (I run my monitor at 1080p, and plenty of people are running even higher than that).
You could convert VGA down to an NTSC composite video signal, and capture that with commodity hardware; but there will obviously be an extreme loss in video quality. You haven't said what your goal is here, so I don't know if that is acceptable or not (probably not though).
This page has up-to-date information on both true VGA capture devices and NTSC conversion; it even gives some devices and their Linux compatibility. Seems a good a place as any to start searching.