D33M3R's procedure worked for me. And I tried all of the programs mentioned here before I used his method because it seemed the most risky (which, I suppose it is, sort of).
I was in the same situation. A user had used a cd-rw's for his backups. He sensed his computer was about to crash so he tried to do a backup, but only made it past the quick format. Then his hard drive crashed. So he was left with a dud HDD and a "blank" backup disc.
I created a 650MB (650*1024*1024=681574400 bytes) blank file in hedit--all you have to do is go new, edit, insert, and insert the above amount of bytes (which allows programs in the future to use the whole area of a 650MB disc). Then i saved the file as 'cd.bin'.
Then, I went into Nero and quick formatted (to be sure), and created a new ISO. I added the 'cd.bin' file to the burn, and went to burn. Be sure to change the burn type to 'disc at once,' because 'track at once' will record your data track first and you do not want that.
Once you're ready, press burn. You'll be able to watch it write the lead-in. I had pressed cancel already and was ready for it to go out of the lead-in when it did. Canceling the lead in before it was done just caused a corrupt allocation table and so i had to re-quick-format and re-burn the lead-in. So I cancled it right when the data track started. I probably lost a little data, but it was all lost otherwise.
I didn't have to restart, i just put the disc back in and it recognized it. It showed it as having my 'cd.bin' file--that's useless to you. You need somthing that looks at the actual sectors. Somthing that recovers lost data. I ended up using ISO buster to extract the data like D33M3R suggests and then using the same program to recover the lost data. Multi-ripper didn't work very well for me. A lot of the files it returned were corrupt. ISO Buster worked very well. I was also using a program called FinalData at this point on the acutal disc since it is now readable by other software.
I should note that it is important to do the "sector view". It will show you where your data is so you can focus on it, but also it can show you where corrupt sectors are so you can skip them. I ended up having a patch of about 5000 corrupt sectors in the middle of my disc, so really ended up working with two sector ranges and recovering to two folders. If you're finding that your reading of the disc is crawling at tens of sectors per minute, you probably have some corruption and should look at bypassing patches bigger than like 30.
All and all, this process was able to save most of the files off the user's backup disc. Oh, they won't have file names and directory structures any more, so that's a bit of a pain. But all and all, given the options, this solution worked very well--if it was a little time consuming.
So thanks D33M3R.