Aha! I took the top of the 3-disc player off and I discovered 4 (!)
discs.

I took them all out and the tray now opens and closes!

I then put 3 discs back in the tray and closed the tray.

But now, when each disc is positioned over the read lens, the disk
doesn't spin (it moves only about 1/2 inch and stops) and "No Disk" is
displayed on the front panel.

Any suggestions?