First thing I would suggest is download the Memtest86+ ISO, and burn it to a disc:
Memtest86+ - Advanced Memory Diagnostic Tool
Boot off of the disc, and let that run overnight (4 hours minimum is good, but the longer it runs the more thoroughly tested the RAM is). This will test your RAM to see if it's bad or not. If it comes back without errors, then we can rule that out. If there are any
errors at all, then you'll need to test RAM sticks one at a time to see which one is causing the issues.
If no errors, then try removing all extra PCI cards and see if you still get lockups.
I would also try running a chkdsk. Do this by going to Start > type in cmd > right click Command Prompt > Run as Admin > type in the following:
chkdsk /f /r c:
It will ask to schedule on next reboot. Type in Y and hit enter, then reboot. Let it run the chkdsk (could take an hour or so, depending on the size of your drive).
May also be a good idea to check the System portion of the Event Viewer around the time of your last lockups to see if there's any indication as to what could be causing it there, as well.