…and installing an SSD at the same time. This particular laptop has served me for seven years already and I would normally not bother, but SSDs are cheap and it will make a good Minecraft rig for the kids. I already installed Linux and Windows 10. God bless KMS Pico.
The problem, as it turned out, was a small piece of ABS from a case peg that had broken off and settled inside the cooling fan. Made the whole rig sound like it was going to explode.