It sounds as if you have done the obvious things. If a thorough cleaning does not allow you to read a disk that has been formatted in that self-same drive, then you have a more serious problem.

From my experience, the next thing you should do is follow up on your earlier observation, and look carefully whether the head is in fact making good contact with the disk surface. In particular, take a close look at the flat copper-ish spring that connects the head assembly to the rest of the drive. Is it creased or torn? If a floppy's metal shutter snags on the head (not as uncommon as one might wish), an overeager user can easily wrench the head assembly. If the head isn't torn off altogether, the spring can tear or otherwise get damaged, preventing the head from properly loading against the disk surface. If the damage isn't too great, you might be able to bend it back into place.