I have a really hard time believing that both the Windows installer and a Linux installer don’t work without there being at least one hardware problem present. But you did swap out most of the parts that I’d think are likely culprits.

Hmm.

When you were swapping parts on this thing, did you have the system either unplugged (preferably) or powered down at the PSU switch? Not just the motherboard’s power off? I remember once accidentally pulling a video card without cutting the actual PSU power, frying both the motherboard and (though I didn’t realize it at the time) the video card, then plugging the video card (correctly) into a new motherboard and frying that motherboard as well, so that even after I swapped out the video card, I still had problems. That is, a damaged part theoretically can damage other parts. Never heard of anyone else hitting something like that, but…

I could imagine that an underpowered PSU could maybe cause a variety of other failures, but you said that you replaced it, and I’m assuming that you checked that it was rated for the components that you had.

Manually underclock the memory in the BIOS as far as possible? Try running with just two sticks (your motherboard manual will tell you which slots to use if you have only two DIMMs)? If the memory’s marginal with your hardware, that will help. Not saying that that’s a fix, but it’d isolate the issue.

EDIT: Maybe vacuum the thing? I guess if you have metal shavings or a screw or something like that rolling around in your case shorting stuff, it could cause issues.