I'd never trust a CD-RW for a backup, so yeah, get some CD-R's. They are cheaper anyway since they can only be used once, and tend to be more reliable.
As for the backup, have you tried opening that backup program again?
Programs I know of have a Recover feature you see, as well as a backup feature that will read the disc and recover what you had on the PC.
This is because they tend to use compressed files specifically made for the program that windows itself might not even be able to read on its own, and so aren't just individual files you can drag off onto the new PC. Once you click recover, it would then uncompress the files back to individual ones back onto the drive the way they were.
Hopefully this will work