I assume from the way you've worded your question that you no longer have a working Amiga you can restore them to, or use to make adf's of the disks?
Hardware-wise you'd probably need something like a Catweasel (
http://amigakit.leamancomputing.com/catalog/product_info.php?products_id=842 ) that would allow you to read back the contents of Amiga-formatted floppy disks on a PC (for use with something like WinUAE or Amiga Forever).
As for the backup software, might it have been ABackup? Good luck!
