Hmm, if it is not the memory, then there are really only two other possible problems. One is the Powersupply spiking because the capacitor is damaged or a has a leak, or the CPU is missing a clock and or the CPU is spiking with higher or lower ticks then it should, which would cause random spurts and lockups. The powersupply sounds like the culprit here, but NOW THAT I THINK OF IT!!
COOLING! If the PC is running to hot, it will lock up as a safety precaution in order to keep from burning up. Certain MOBOs have a failsafe, because when a CPU hits a critical temp, it spikes and misses ticks, or strains to perform at that speed, so the processor does a primary memory dump in its Cache to stop the stress, then resumes (sometimes) after a cooldown.