When you try to play a song in your new library does an exclamation mark appear next to the song's title?
If so, that means that iTunes can no longer find the file for that song, because either:
- it is no longer in the location is was in when you added it to your library
- the file has been renamed, moved or deleted
- the path to the file has been renamed, moved or deleted
How did you add the music to your new library? If you simply told iTunes to add what is on an external drive, then that drive needs to be connected and ready to read before every time that you open iTunes.