The good news is, my Intel iMac is back from the shop and operational again — and in about half the time I expected it to take.
The bad news is, there’s a new problem: the fans are going full-blast, and the normally silent iMac now sounds like a jet engine. Resetting the PRAM and the SMC has no effect, so it has to go back to the shop. (Sigh.) At least it runs, and I can access my data, even if it is just a little bit deafening.
My working theory is that a heat sensor has been disconnected, and the computer is compensating by running the fans at maximum. We shall see.
An hour on the phone with AppleCare. It costs money, but they do look after you.