The vid card is trying to protect itself. You need to do some research on that card using google and re-seat the cooling. Anything over 90c on a vid card can force the computer to shut down... in fact I'm not sure that card would get over 90c with 25 percent fan. Did you buy the vid cards used? Did you flash the bios on the vid card to run out of spec? The other thing that can cause a computer to act flakey is a failing HDD.
So you need eliminate possible causes. Unplug all hdds except the OS drive. Remove all ram except one. Run on the good video card and then on the bad vid card. You wanna try to get your computer stable and then recreate the problem buy introducing hardware. Don't the 4870's have a vreg heat issue?