There are basically two types of DVD media you can use to burn an ISO image of Knoppix on. They are called DVD-R and DVD+R. I have got an old notebook that does not boot from a DVD-R, but I can use a DVD+R medium. Therefore my first idea would be to create a new Knoppix boot DVD on the other type of media.

Another approach would be to download a recent CD version of Knoppix and use a CD-R because I never had issues using a CD-R.

My last idea would be to clean the lense of the LASER diode because I had recently to do so since my DVD drive did not boot from DVD anymore. I used a cotton bud and isopropyl alcohol. One has to be careful not to apply too much pressure in order to avoid irreparable damage.

Since you only want to copy your files from your internal HDD to an external one any version of Knoppix that can read NTFS should be appropriate if the files are on a drive with NTFS.