If so, can I play Doom 3 in safe mode?
No, safe mode disables video drivers
Even with windows using that RAM, it shouldn't cause it to fail, it'd just be sluggish, try turning your aperture down to 64mb.
BTW: Prime95 puts your CPU at full load which makes it draw off that rail. So you need to run "stress test" in prime95 and choose the "Large in place FFTs" option, then using a program like motherboard monitor 5, see if any of the voltages take a sudden plunge.