Did you check the PSU? That sounds like the culprit actually but first check some other things...

I didn't actually and it's one thing I fear the most, as the PSU was quite expensive. And also shipped from quite a distance. Are there any telltale signs that it could be the PSU? Things to check, other than trying a different one / trying this one in different rig?

Do you have a bios speaker, and if so, did it beep when it didn't want to start (when you were moving the RAM)

No BIOS speaker sadly :/

Probably not it cause you said you cleaned the stuff up, did that mean that you removed everything and put it back in. If not is there the option that there is something behind your motherboard causing a short?

I removed and reseated everything a few times already, except the motherboard. I might have to go and try that one as well, then.

When you remove the CPU, do you notice any bend pins?

No bent pins, looked a few times, even through the watch-magnifier thingy.

You didn't mention it so probably not but do you notice any time or date problems on your pc (not showing the correct time/date)

Not in windows itself or in BIOS. I did also reseat the CMOS battery once (that one time there were time problems, obviously).
But there is a strange thing which happens after numerous crashes in a row (8+) and that's when I start up chrome afterwards, the "Recent tabs" and history sections are all messed up, incorrect dates and days on things, future dates and so on. It clears up after next chrome restart.

When checking the motherboard do you see any leaking capacitors? (Looks bigger with some yellowish stuff on top)

Nothing like that. Everything looks like right out of a box.

Thanks for the suggestions, I will try to reseat the whole motherboard and perhaps try something with the PSU.