Memtest86+ - Advanced Memory Diagnostic Tool
Download - Pre-Compiled Bootable ISO (.zip) is the one you want.
Download, unzip, burn to a disc using the Burn Image tool.
Turn off the PC. Take out all but one RAM chip (testing them all at once will take forever).
Turn it back on, make the boot run from the CD/DVD ROM first, and run the tool. Let it run the tests.
If it all comes back fine. Turn off the PC. Take out that chip, and insert the next, and repeat.
Hopefully you will find a culprit. If not, it is something else, but this is a good starting point.