Not at all helpful, but that doesn't stop anyone else: I once had a brand-new 5.25" floppy diskette that kept coming up "not ready" in every drive and system I tried it on... could not turn the disk at all - as if it were square! had us all baffled, until I dissected it and found that excess glue had been applied to the jacket flap and had glued the disk to the jacket.
Is that a new diskette, or could it have been contaminated before? Is this the first time you've tried to use this drive? (could the drive head or mechanism have been serviced by an auto mechanic that thought copious amounts of grease solves everything?)
Typically, floppy drives have a hard-stop to prevent the head from moving past the outermost/innermost points. There should be no way to get the head to move into the spindle - which should not be greased anyway.