Update: Using info from the Repair Manual (thanks!!!), I was able to get the unit into a DVD diagnostic mode. In that mode, the screen would open for both CD/DVD and SD access. I could open and close it repeatedly with no problems. However, it wouldn't ever open without going into that diagnostic mode. Weird.
I'm shipping it back now for repair or replacement. Maybe someone smarter than me can figure out what is wrong. Obviously, there is no problem with the mechanism itself.