In case the files are missing on new computer or you cannot find the tracks when launching the itune follow the easy steps below.
The following assumes that the old computer still works and has all your tracks on it.
On the OLD machine.
1. Launch iTunes, go to File > Library > Consolidate Library. (This moves all your tracks into the iTunes Library.
2. On completion, select ALL of your tracks and drag them to the external drive.
On the NEW machine.
1. Download, from the Apple web site, and install a new copy of iTunes. Launch it and then close it. Incase if new version of itunes already installed then skip this step and follow the steps below
2. Connect the external drive to the new machine
3. Launch iTunes, select Import to library, navigate to the external drive and the folder in which you put all your tracks. Choose that folder. Sit back and watch them all come into your new iTunes library.