Download Memtest86+
from this location here. Burn the ISO to a CD and boot the computer from the CD from a cold boot after leaving it off for an hour or more.
Ideally let it run for at least 7 passes / 6-8 hours. If errors appear before that you can stop that particular test. Any time Memtest86+ reports errors, it can be either bad RAM or a bad Mobo slot. Perform the test RAM sticks individually as well as all possible combinations. When you find a good one then test it in all slots. Post back with the results.
See
this Guide to using Memtest 86+