Desktop and taskbar looked normal, mouse could select things, but clicking an icon had no effect at all. Explorer had stopped running. When I decided I needed to reboot, Ctrl-Alt-Delete also did nothing so I had to do a hard power off.
I leave my Windows 7 PC running all the time. For two days in a row I had that weird situation first thing in the morning. Never had happened before.
Eureka, solved:
Clearly something was happening during the night. Finally I though of a task I had scheduled, a batch file to copy some files from one drive to another. The thing is, I had installed an additional internal hard drive and disconnected my flaky USB external drive. My batch file was stymied when it tried to address non-existent drive, and evidently paralyzed Windows. The mouse worked because mouse input and navigation are handled by interrupts, but nothing could execute.
I removed the batch file frorm the Scheduler and the weirdness is gone.

I'm posting this because I didn't immediately think of error in a scheduled task as the root cause and perhaps I can save someone else some head scratching.