Remote Desktop doesn't work!
I just had a chance to try it with a third computer. This one is remote (not local LAN). It was using just a PIN. The symptom was that I could log in, and then my view of the remote computer froze. I could see the desktop, but the Remote Desktop window was showing. This window normally disappears when you remote in and a connection is made. It is replaced with the small RD toolbar. In this case, the toolbar was not evident. Also, the person at the remote computer said I was moving things around, but nothing was updating on my screen.
Based on this observation, I can now say that the symptom in all three cases is identical. What happens is that I am able to log in, and then the local view of the screen locks up. My mouse and keyboard are actually working on the remote system, but my view of the remote system is not updated.