OK, I pulled the thing out (thanks) and took a look. Checked connections, which looked OK, then 2 weird things happened:
1) With 2 plugs undone, (a small plug about the width of a pen, and part of the bundle of colored wires), the radio powered up, then later clicked off, as usual.
2) I then reattached evertything, then tried the "drive the car for an hour, then turn on the radio" suggestion on another part of this forum, and the radio has worked.
The ironic part": Part of running the car for an hour meant driving to the car audio shop. Maybe the radio "knew" it's days were numbered, and decided to behave.
Any thoughts from anyone?