You'll need FAT partitions on that external drive, Linux can't write to NTFS (A little gift from Microsoft).

If you have or make FAT partition space there:
  • 1) Boot Knoppix with the external USB drive attached.

    2) See if you have desktop icons for the internal partitions that you need to recover files from (without knowing what happened to the disk there is no way for me to know what happened to the drive or if the partiions are still there).

    3) Click on the partitions and see if you can find your needed files.

    4) Confirm that you have desktop icons for the external drive and the FAT partition(s) on it.

    5) Right click on the external partition icon. Use the actions... sub-menu to make the partition writeable.

    6) You can move the files between the partitions any number of ways, including drag and drop.

Give that hardware can fail and Windows will fail and cause exactly this, why would you have no backups?