While gaming on my computer, sometimes my graphics driver crashes and recovers, and I can still continue playing whatever I was playing, although with a severely reduced framerate. Other times, I'm finding my computer emitting a loud, shrill continuous beep, which doesn't match any beep codes I've looked up, and then it crashes. No sound, no artifacts, it just goes kaput, and I need to reboot it. Could these things be related, or perhaps they are two separate problems?
I had the same issue before with my Radeon 4830 when playing Amnesia the Dark Descent. After about ten minutes it crashes and then recovers but my game is still frozen and not responding. I tried many tweaks but to no avail. So then I changed/upgraded to a Radeon 7770 graphics card and BOOM everything was fine and NOT even a single time it has ever crashed.
So I would say you may have to give up on that graphics card and buy a different one.