In front of the floppy drive, you have got several micro switches (3 if i remember clearly) one of them is there for floppy size, the second one to detect floppy protection and the last one is a floppy detection.
So the drive is able to know the size of the floppy (400 k / 800k /1.44 k) if a floppy is protected and if the floppy is present or not.
If one of them got stuck, you can have those kind of troubles.
try to remove the drive and lubricate it, will probably be fine afterwards.