It might be just a loose connection. Re-connecting everything has fixed the problem for now. Since nothing was moved that could have loosened connections, a slight element of mystery remains
The external storage I have been using for backups does not respond to the power button. It was fine when I switched it off this morning.
The power light on the brick shows it's getting AC, and it is plugged firmly into the drive, which exhausts my troubleshooting repertoire here.

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