I've been having a very frustrating PC problem for multiple years and I'm getting to the point where its becoming intolerable. On my Windows 7 machine I experience seemingly random total system freezes (as in the screen freezes and the whole system becomes completely unresponsive to anything), outright immediate reboots, as well as BSODs with completely different error messages each time. This has been happening for a long time and I've been totally unable to discern a cause, be it hardware, software, driver, or anything. The only thing is that it seems to be more common while the system (either CPU or GPU, not actually sure which) is under load, as its rare normally but incredibly common while playing most 3D PC games (doesn't matter what game).

Now I know my problem is incredibly vague, so I certainly don't expect any of you to be able to just diagnose my problem. But I'm here because I have absolutely no clue how to begin troubleshooting this. Can someone please point me in the right direction here? What do you guys do when you have a problem like this? I've already tried the obvious solutions like updating drivers, checking disks for errors, etc. I don't know how to do things like read BSOD memory dumps though so I'm stuck (and when my PC freezes I don't get one of those anyway I don't think). What should I do?