If the drive reads all floppies as write protected, the sensing mechanism doesn't work. This is fixable at home, if you have a soldering iron and can handle two very small components.
The disk is marked as write protected using a hole in the corner of the plastic cover. The drive senses the hole using two protruding plastic pins right behind the opening, to the right. If the disk has an open hole (it's write protected), the pins can go a bit further up than if the write protect lock is closed. The plastic pins are seated in a plastic holder, inside which they rest on top of a V-shaped metal part which flexes. If the pins reach the closed write protect hole, the V is bent together, causing contact for an electrical signal. In your case, the metal V is dirty and doesn't establish any contact.
What you need to do is to desolder the sensing mechanism (it's 4x4 mm or so) and disassemble the black plastic holder. Take the bent metal part and clean it with a fibreglass brush or alcohol or whatever you have at hand, and reassemble the drive.
