Hi Snoids, It's me again.

Been there, done that. It sounds like the same thing that happened to me. The SY77 has a rubber belt in it that turns the drive reader which allows it to read the disk. I suspect that belt is broke. So the motor is turning and making the appropriate noises but it isn't turning the reader to read the disk so it never finishes. I took the back of the SY77 off myself. Took the drive out and saw the broken belt. I then had to find an electronics specialty type store that told these kinds of belts and I bought a few different sizes. They don't cost a whole lot.
I put it in myself and it works perfect now. I would bet you money that's your problem.
Because everything that is happening to you happened to me. I, too, had to turn the synth off to unlock the drive.

I can also show you a way to use midi so that you never have to do this again. You will never need the disk drive again. I researched and found this technique because if anything ever happens to the disk drive, all my songs would be lost. I understand that Yamaha doesn't support the drive any longer. And a normal disk drive won't replace it.