Is it overclocked?
Check the system logs again, and look for a memory dump. It might not show up as an error, just a report of a dump or a mini-dump.
If there is mem dumps, the memory is either bad, or is overclocked too much. I had this same issue, and first blamed it on my old 300W PSU thinking it was being overdrawn.
Found the dump errors, and tested the memory. Memtest ran for a few minutes fine, but a Eurosoft PC Check test failed both sticks running at 208 mhz. I down-clocked it a little so they would run at 200 mhz (DDR 400) where they're supposed to be and they both passed, and havent had a problem since.
I guess Patriot RAM doesnt like to be OC'ed.