I don't have any experience working with tape drives, but I was basically going to say something along the lines of what Mark said.

My educated guess would be that any belts in the system are long gone. The MSX computer used a pulley-based belt system for its floppy drives. Those belts just disintegrate into oblivion over time and need to be replaced. In addition to replacement of the belt, the floppy needs a good cleaning. Those belt pieces could be anywhere, and they most likely left some residue around the wheels.

If any belts or items are gone, it is possible that issuing commands to the drive will cause it to still make noise. That's a start. If that happens, maybe it is only a matter of replacing belts (assuming they are there & it isn't simply made up of gears). If no noise is made, it could be that a motor is burned out or the tape cannot be communicated with properly. I am totally guessing here. I would love to mess with it, but this would be for curiousity and experimentation moreso than applying experience to "just another tape drive repair."

While I haven't serviced a cassette drive (aside from extracting old tapes from one), I can say that they have an awful lot of mechanical components in there. Not sure if you want to "experiment" with this one too much as it is tough to come by.

If someone is to take that thing apart, they probably want to take good macro pictures as they move along in the process - both for historical documentation purposes (rare device!) as well as a reference for reassembly.

Good luck!