Is this by any chance a very old 3.5 floppy drive. I think they were 780K drives. If so it is the diskette that is the problem. Your new floppy drive & old floppy disks are incompatible.

Strip your old floppy out of the old machine & put it in the new one. Make sure in the BIOS you set the correct drive type. Then you can read old style floppies.

I think I have heard of utilities that read old 780kb diskettes on a 1.44mb drive. Can not remember where though.