What kind of music files are you backing up? This doesn't sound like you are moving a common music file like an mp3. Instead it sounds like you are moving some sort of downloaded, copy protected media. There are certain music sites that have copy protected music and along with those songs, a media license is required. Many times that music can't be easily moved from pc to pc, even with the license files for a simple reason...it is copy protected to keep people from giving the music to their friends or sharing it online.
If this is a case of copy protection, then you need to find out where the music was bought from and find out what their rules are for moving the files from pc to pc.