I'll try to be as concise as possible because I have a lot to say about my problem, but I'd rather say it when asked or when I feel it's necessary, just to make this initial reading clearer.
For about a year and a half I have periods when my system has all the problems in the title (I'll use the word 'crash' for either one). I'll list some patterns and what I tried to do and what were the results, but the list is not exclusive:
usually it crashes when a CPU-intensive operation is in progress, like a game or video encoding or HD movie rendering, but also sometimes crashes when I'm doing nothing
after a first crash the system is very unstable and sometimes it crashes even during POST, or doesn't boot at all
Some months ago I went to a local service (one that you just put your computer on the table and sit there with a guy and trying to figure out the problem, very rare these days) and they used OCCT and it crashed every time he changed some part to test it out (PSU, RAM, video card, HDD). The last one was the CPU. They changed the CPU and it didn't crash any more. Then when they put my CPU back, it also didn't crash. We figured that the trouble was the thermal paste (probably some 2 years old) because it was the only thing changed while testing.
Up until 2 weeks ago, I haven't had any more problems. 2 weeks ago the problems reappeared. I changed again the thermal paste, put some Arctic Silver 5, and for about a week everything worked perfect (tried some games, video encoding, no more crashes). But again it started crashing in the same fashion as the first time.
But now, instead, I figured out a very odd behaviour:
when I start some of the apps above, in most cases it crashes
if I start OCCT and turn on the CPU test, and run any of the programs above, it doesn't crash, even if the CPU is on 100% load (and 65-70 degrees Celsius temperature)
if I shut down OCCT and continue using the programs, it crashes in a very short period of time (even if the CPU is on 5-10% load and 40 degrees)
There are so many patterns and temporary solutions that I figured out in this year and a half period of time, that I can't include them all because I don't know which one are more relevant, but I'll happily provide any details you ask.
My system is:
CPU: AMD Phenom II X4 965 (3400 MHz - 125W)
MB: ASUS M4A79XTD - EVO
RAM: Corsair Vengeance 8 GB (2 x 4GB) CL8 1600MHz
Video: HIS Radeon HD5770 1GB
PSU: Corsair 750W
HDD: Western Digital 1TB
OS: Win 7 Enterprise 64 BIT (also tried with Windows Server 2008 R2 Trial and Win XP)