If you dont mind a copy of your tunes being also on the new PC hard drive, you can install iTunes on the new PC - You create an account and authorise the new PC (You ar "allowed" 5 PC's) If you want you can de authorise the old one.
Then you copy your tunes from the external disc into the new music library.A copy stays on the external drive. This way your external drive acts as a back up. You can have several libraries, but that is not what you asked. Not sure if this is what you want.