Solved.

I thought the hard drive was overheating due to age, but it was just a question of removing the ball of dust from the top of it.

DAMN! How long has it been since you did a thorough cleaning of your case and components!

That is one friggin' big dust bunny!

It is huge, indeed. It's actually not my machine, well wasn't, it was my brother's server from one of his shops. He replaced it with a new one due to poor performance, although had he given it to me to look into first he could have spared that expense, I believe. Anyhow, I'm known as the guy who willingly accepts donations of old hardware so I saved the server from the trash bin, and found pretty much exactly what I thought I would...about ten years of dust.

Wow, now that's dusty! I clean my PC out about once every 6 months or so, but it turns out that my GPU fan duct was almost blocked last time I gave it a spring clean - thankfully I caught it before it overheated.

Yikes!
If it moves, shoot it!

I think I saw it move in that picture!! YIKES!

All I can say is ... WHOA. Yeah, for quite a while now I've realized that it's extremely important to open up your case at least every few months and clean it out. I'm amazed at how much stuff accumulates. Up until now I've just been buying bottles of compressed air, but I am very seriously considering buying an electric blower instead, figuring it would be more economical in the long run and do a better job.