I may cry. My fan on my PC stopped working (it's an iBuypower water-cooler and it still goes through the motions, but it's no longer cooling), so I got some thermal paste to see if that was the problem. See inside for more of the tale of panic and woe.
I heard a loud noise when I released the first screw (it took a lot of effort, but it didn't look as if I broke anything) but managed to get it off and then put on the thermal paste. Doesn't go terribly smoothly, but it's on. And then I try to rescrew everything back in. Which does not work.
Anytime I manage to get any of the screws what seems to be in, I try for one of the others and the first pops out again. I try to screw all four evenly and nothing. I try to do opposite corners and still nothing. I'm at my wits end.
Also the room I'm in doesn't get the best cooling and so now I'm overheated, exhausted, and still have no computer. Even less of a computer than I did have, since technically it would run for a little while before the heat started getting up to 70c running nothing but Firefox.
So if anyone from

was wondering where I'd got to...
a few months ago I bought a USB fan off of amazon that seemed to do the trick. I took the panels off of my tower and directed the fan into it and it seemed to help. It wasn't that expensive if you need something in the interim
it's also doubled as a nice accessory to point at me during this heatwave fwiw
I mean, I can always yank the fans from one of the other dozen PCs that are around if I need to, but it's that whole 'not screwing to the motherboard' that's causing the issue. If I can't get one, I likely can't get the others.
...i'm very puzzled what could have broken that would make all the screws unable to thread like that O.o
So. Considering that I've never done this before. Is the threading attached to the motherboard or would it fall away if they were unscrewed? I left the motherboard attached to the PC.
I can take it off if I have to.
honestly i'd be reluctant to guess without seeing it myself, since
in theory it could be either way
I mean, I could send a picture of what it looks like at the moment. Or I can tell you the motherboard. It's a ASUS PRIME Z690-P D4 w/ WiFi.
The manual isn't saying anything about needing to look underneath, so I have no idea what I'm doing wrong.
Not holding it down enough, maybe? I dunno.
Hah HAH. Success. There WAS a backplate that fell off when I let all the screws go.
I've cleaned the CPU again because the thermal paste had since dried and the CPU and fan weren't sticking together anymore. And then I replaced the fan the RIGHT way and it went in without too much effort. Now I may crash because I've been worrying about this all night and now I know that if I need to change to another fan, at least I have a manual.
I will check it out when I wake up to see if it's really working or not.
samame: Thank you! Also, I poked you elsewhere since you never replied (to my belated reply, which is understandable on your part).
Exacerangutan: Thank you, by the way. You saying it should have worked caused me to look for reasons it didn't.
Now here's hoping that's actually the fix for the problem and it's not the fan being dead.
ohhhh that makes sense! and yeah sorry I didn't have actual answers, but I'm glad my pedantry rubbed off enough to be useful XD