Another non-obvious possibility is that the disk jacket itself has
been pinched around the edges and the extra friction is keeping the disk
from spinning in the jacket. If you need the info off the disk, cut a
small margin of the jacket off around the edges or you can remove the
internal disk itself and put it in a known good jacket (cut just one end
of the jacket for the disk to slide back into the jacket). Experiment...
Or just _carefully_ slide the bare disk into the drive (with the drive
out of the case, so you can centre it on the hub) and copy the data off.
Over here this is generally called 'mounting a naked floppy' :-)
-tony