Hi Techx,
I understand totally how you feel, becoz i've suffered numerous episodes of frustration with amiga diskettes failure....
In your case, there're three possibilities:
i- the magnetic field had indeed caused damage as you yourself reckoned;
ii- most of the disks had already gone bad since they were left in closet for years;
iii- the disk drive in your A1200 is no longer mechanically sound since it's been left unused for long time, as suggested by ddniUK.
You can try a disk cleaner kit to clean the read/write head of the drive; failing that, buy a new disk drive.
For me, 90% of my diskettes are corrupted by fungus (due to the warm & moist air in the tropical land where i live)
I recently managed to salvage some endeared disks by painstakingly wiping out the fungus with cotton swaps + alchohol... Hours of work over several weekends.