It was not the mouse. However my problem is solved, although I am unclear precisely what fixed it.
I took the MBP to the small Italian town of Macerata, near where I am working.
http://www.medstore.it/assistenza/#esperienza_hook
They offer technical support. It was fixed in about 5 minutes. It was one of those situations when someone takes over and you don’t ask, just hope. Thank you kind man in Med Store. I will try and find you so that you can join this discussion and tell us what the problem was and how you fixed it. Grazie!
If only you had said you were in Italia, we all know that the hands are nowhere near the conversation!