Checking the memory should be first thing, especially with this symptom.
Also, just to help in the guessing game of which piece of memory it is (assuming you have more than one), try turning off the computer, and immediately after tuning it off, carefully unplug the PC, and feel the memory DIMMS. If they are both the same type, but one is hotter than the other(s), then try running with only the hot one - take the other one(s) out, and put the hot one in the first slot if it isn't already there. THEN test the memory to see if that's the culprit. If it is, you know which DIM is bad, assuming it's only one.
I suppose it's not a real scientific test, but it seems to be pretty accurate when I've tried this to narrow down the specific culprit.
Oh, and as BadBigBen has mentioned in another thread recently, any time your messing with your PC internals, be sure to do something to negate any static discharges from YOU. For isntance, touch something metal... use a PC work type anti-static wrist strap if you have one.