Maybe a long shot, but I once had a similar problem with one of my geforce cards. When I first loaded windows, with NO drivers yet installed, it worked fine in the crappy generic display mode. Once I loaded the Nvidia drivers, then I got problems. It would lock up, get garbled unreadable display, and just act generally crazy. Although for me, I didn’t have to play a game for the problems to happen, even in windows it was screwed.
Turned out that I just needed to reseat the video card, not all the connections are always being used. Probably why it would only fail when hardware acceleration was introduced, certain circuit pathways were then trying to be used.
So maybe one of the contacts on your card is not making a connection, longshot like I said, but maybe. You may also want to clean the contacts while you have it out. A good trick is to use a pencil eraser to gently wipe the contacts. It is known to be very good at removing the carbon buildup, which is sometimes what makes a contact fail. A qtip and some alcohol will usually work too, just make sure the contacts are totally dry before you try putting the card back in. Try not to touch the contacts, or any components on the card too much.
Also make sure the fan on your card is turning, cause you might have an overheating problem as already mentioned. Also you didnt say what drivers you’re using. Try the Nvidia drivers from their site, they’ve always been trouble free for me. Or maybe your vid card is toast, or possibly your motherboard. It could even be just bad RAM memory, I’ve seen that do some REAL crazy stuff. Good luck!