I don't know what to tell you. I don't doubt what you are saying is true but obviously no one including myself has seen what you are describing.
I suspect the answer is there and simple. I guess I'd try the Seagate disks in another computer just to be certain that they will boot and take you to the DiskWizard program.
I'd maybe try another floppy drive in your machine. Maybe try a new floppy cable. Maybe try setting the floppy to B: in the BIOS and then moving the floppy to the correct connector on the cable. Try removing all but the minimum memory or try known good memory from another machine. Try disconnecting the HD and then booting to floppy. Removing any extra cards and devices and running the machine as stripped down as possible. These are all just suggestions because something is very VERY unusual here.
Maybe you do have a bad Mobo or floppy controller in addition to the likely bad HD.
I said I'd suggest another utility to zero fill your HD. It is available for fully functional trial at:
http://www.east-tec.com/sanitizer/
Again, you download it and then run the program to create a floppy which you then boot with and follow the directions to run a complete sanitize of the disk.