Knoppix can usually access an external hard drive, a newer version may help. But keep reading before you rush to do this.

If the external hard drive is formatted as FAT32 then you should be fine. But if it is formatted as NTFS then your version of Knoppix certainly can't write to it. Some people believe that the newest versions of Knoppix can safely write to NTFS, but I personally would not risk this unless the drive was empty and just being used to transfer the files elsewhere. Backup the NTFS drive files before taking any additional risk.

A much cleaner way to recover files with Knoppix is across a wired network. install a FTP server on the system that you wish to send the files to. Boot Knoppix on the bad system and confirm that you can ping the destination system. Then use Konquror as an FTP client to send files to the other computer by FTP.