I can't find anything for a PC that would let you grab DVI and turn it into a digital format the PC could use. Certainly it wouldn't fit on the PCI bus (133MBps) -- at 1600x1200 30FPS you're talking ~1600x1200*24*30 / 3 ~= 500MBps of data. Even at 1024x768 you'd be pushing over 200MBps. PCI-X could do it, maybe, but there don't seem to be any products available. DVI is only an "output" format; professional equipment (other than monitors) doesn't really handle it, because you'd never use it for connecting editing equipment.
Best it seems you could do right now would be to get an ATI card with a VGA->component adapter (or get an external transcoder), then go component->HD-SDI (via another transcoder), then get a professional-level HD-SDI capture card. Not cheap, though, and you're still only talking 1080i/p or 720p.
There seem to be VGA capture devices out there, but I'm having a tougher time finding solid information on them.