I would start right now, I doubt that both your sticks of memory went bad, so take out one stick and run it on the remaining stick for a long time to see if it does it again, if it does then put that one back in and pull the other one and run it, if it does it again now, then move on to the other possibles, but you have to start somewhere and memory is the easiest place to start.
make sure you unplug the computer before you touch anything in there.