Blue Screen problem, seemingly at random - error 0x0000007E

Hello, I have a problem with an old computer in that I get Blue Screen seemingly at random throughout the day. It may happen just once or 3-4 times a day. The errors I get are different, here is a picture of the last one.
Attachment 395975

Output from DM Log Collector:
Attachment 395976

The system specs are in my profile.
So far I have:

1) Reinstalled Windows on same HDD;
2) When this didn't help, I replaced the HDD and reinstalled Windows again - no change;
3) Replaced the RAM - no change;
4) Ran tests on CPU, FPU, memory, cache and disks - everything seems to work fine, except about 1 minute into the FPU test the program module crashes (but I *don't* get the Blue Screen);
5) Scanned the disks for errors again and again - CHKDSK doesn't find any problems.

This is getting pretty annoying. Can someone please help?
Thanks in advance.

No one really knows what may fix the problem?

P.S. I I installed Linux on another HDD and there are no problems with it so far, so it seems it's not a hardware issue.