Are you certain that the external drive is formatted as a Mac disk rather than as a FAT32 Windows formatted disk?
To determine, get info on the drive and confirm that under "Format" it's listed as Mac OS Extended or Mac OS Extended (Journaled) This is critical because a Mac cannot boot from a Windows format disk.
If this is not the problem, give Disk Utility a try. Under the restore tab, specify your original disk as the source and the external partition as the destination and then click Restore.