Back in the mid-aughts, I had a really expensive gaming PC which crashed randomly for seemingly no reason at all. It went on like this for about a year and a half at least, and eventually I got so tired of this I spent a whole lot of money buying an entirely new PC with entirely different components in it, only to be plagued by the exact same issue with the new PC as well.
...This was unsurprisingly extremely vexing for me, and I was initially lost as to any sort of explanation, other than perhaps being haunted by evil spirits, or cursed by some god I'd angered or somesuch.
However, it turned out to be a faulty DVI LCD monitor which was the root cause of it all. The one common factor between both computers. I couldn't tell what exactly in the monitor caused the problem, but after replacing it under warranty everything worked just fine afterwards.
Sometimes mysterious issues can have unexpected causes. Don't exclude anything.
Also, surprisingly commonly, random computer crashes are because of bad power supplies. If you haven't tried replacing yours with a spare you got laying around, perhaps you might want to consider it...