Seems pretty clear that your memory has problems.
Start by running Prime95 for at least an hour. That will often reveal memory errors.
If that doesn't work (i.e. it doesn't get any incorrect results), run Memtest86 for 24 hours (you need to create a boot device with it - search and you'll find instructions on how).
Once you've established that there is a problem, you'll want to narrow it down by using progressively fewer sticks to isolate the bad RAM.