Yes, it's Stardock Fences.

I'd feel hesitant about posting in their forum because they may feel uninterested in helping me make an early free version work when they'd really like to get $10 out...

Thanks. That didn't help because I couldn't see any icons on the desktop in safe mode.

However I did figure out the culprit was Fences v1, which I should have thought of immediately.

I had been...

Win 10, 64 bit, recent upgrade from Win 7.

Beginning this afternoon, all of a sudden, the icons on the desktop will not drag, they are fixed in place.

I can delete them, open them, move them...