Even if it's full, should let you access it to copy the files. Most likey the floppy or the drive went bad. Those things are not very sturdy. Try it on another computer, maybe 2. If those don't work, you can pretty much say the floppy disk is bad.
If you have other floppies, I suggest you move the data off them to something more durable like a CD/DVD or flash drive. Not to say that those are fail-proof either, but are way less likely to die than a floppy.