The issue with the hard dive sounds like bad boot blocks, mostly a software issue. Do you have a Boot Floppy Disk with Disk First Aid or Norton's Emergency Boot Disk? Run Disk First Aid or Norton when it boots up.
The Floppy drive is harder to diagnose, as it can range from a misaligned or broken heads, floppy drive needs to be cleaned out, bad floppies, or Bournes Filter has crapped out.