Got a 6800GT PCI-E, installed Test Drive Unlimited to find that after a couple of minutes the screen began to look 'snowy', and various other graphical corruptions appeared. I assumed it was the game, but then played Far Cry, and found a similar 'static TV' effect happening. The PC would sometimes crash and restart at this point, one time with a 'memory error' box coming up in Windows after the reset.
The problem seems to have got progressively worse, Windows was initially not affected, but then fonts/icons become unreadable, and then boot screens were corrupted as well.
As it stands at the moment it won't get past booting, I cannot see anything on the screen to try and diagnose the problem. I thought it may be to do with temperature, but I have a Zalman after-market cooler, and this has always seemed to keep temps down (I don't overclock it btw). However, I have removed the card, dusted off any collected crap and put it back in to no avail.
I'm really hoping the card isn't buggered but it is beginning to look that way :S Seems strange because it has never shown any problems before, and after installing this game has gone from fine to dead...But then it appears to be a hardware rather than software problem.
Do you have a spare PCI-e graphics card? Maybe a friend with one? If you can, instal a different video card and see if the problem persists. If you still get the errors it could be a problem with the motherboard. I guess it also could be something up with the RAM, maybe try running Memtest also.
Reading the first part made me think the problem existed within Test Drive Unlimited which is notoriously known to be bugged. But since you say it also happens with other games and gone to the point where it wasn't bootable tells me that probably it's time for the 6800gt to go. Although it would of course be best to verify, i agree, try borrowing a friend's gpu and see if it still persists.