It's not clear to me exactly what you have done.
What do you mean by the expression "music library" and when you state that the music files are on a separate drive, separate to what?
Your music library (the files) will have hopefully all been in one parent folder, together with the iTunes .itl file (together with the required associated files), which tells iTunes where everything is located. Even if those files are in a separate hard drive to the iTunes programme files, then as long as the .itl file is in the same parent folder as the music, you should be able to add that complete folder to your new computer and with a little work, get iTunes to recognise that old itl file. It will require that the path from the computer to the drive is the same, including the drive letter.
(For reasons I've never understood, my itl file is in an old iTunes sub-folder. I'm very reluctant to touch it.)