easiest to delete your original Library file (with iTunes closed) open iTunes up, and Add To Library using the external files to rebuild it from there. In preferences check the Advanced box "Copy files to Library when adding" and any future files you add from elsewhere will be copied to the external (that you've already set as the home for the Music folder) - any cds etc you rip into iTunes will be copied to the default (now external) folder in any case, same for files you Convert.
iTunes is smart enough to know when you move files, to update the references to where they are, but it doesn't work when you copy them (eg to an external drive), so all of the Library references are wrong and if you've got lots of them, it's easiest just to start again.