I would first rule out a bad stick of memory by installing just a single stick in the 1st memory slot and running Memtest at boot. Let it run for at least 4 passes. Repeat for each stick. It does a much more thorough job of memory testing that Windows Memory Diagnostics. http://www.memtest.org/#downiso
Download the bootable .ISO and use it to make a bootable CD that you can run at boot-up.