I recently fixed a friends PC that was crashing like you are describing, first thing to do is find out if its just D3 or other games, what i did was run a program called Furmark and run it on the res of your screen but turn all AA on to the max, this will stress the gfx card out to the max, if that crashes aswell you know its not just D3 thats the problem.
As said above, try a total clean install of gfx drivers by removing old drivers and doing a clean install of new drivers, use a program called msi afterburn to check gfx temps etc see if anything looks out of the ordinary, Also check you have the latest drivers for your motherboard.
For my friend i tried EVERYTHING, and was convinced the PSU or GFX card were broken, until he put his GFX card in my pc and it worked fine, so i was thinking it was the PSU, it actually turned out to be the BIOS was out of date, So i would check that too!!