A new motherboard, and he's good as . . . well, NEW!
I'm pleased to report that all peripherals are re-connected, up and running. All internals seem to check out. Nothing was lost from the hard drives or the backup.
The Dell technician did it all in about 90 minutes. It was old hat for him. I tried not to let my awe show too much.
So, bottom line is: I suffered the inconvenience of having to share the laptop with Carol (much to her disgust) for 3 days. Not a penny out-of-pocket. And now Carol is much happier to haver HER machine all to herself again.
Not bad, Dell!