That really depends what's wrong with the drive, but you can repartition and reformat it after you get your files to find out if it is usable.
Knoppix can't mount those drives? Do you see icons for them on the desktop? If you do, you may need to use the right-click to either change permissions or mount the drives before you can access them.
But if the file structure is too far damaged, then Knoppix won't be able to mount them. In that case, we are back to the PE in order to run recovery software to try to get the files. Or, connecting the drive to another machine, which would really help recovery and testing the drive.