That won't get your your "library". Your library, in essence, is (was?) a file called library.itl in your iTunes folder. This is a database with a listing of which media files you have and where they are, long with playlists, ratings, and a bunch of other things (which artwork goes with which album). If all you have on the external drive are the media files then when your old computer died it took the library.itl file with it.
What are the iTunes library files? - http://support.apple.com/kb/HT1660
More on iTunes library files and what they do - http://en.wikipedia.org/wiki/ITunes#Media_management
What are all those iTunes files? - http://www.macworld.com/article/139974/2009/04/itunes_files.html
iTunes 9 [and later]: Understanding iTunes Media Organization - http://support.apple.com/kb/ht3847
Image of iTunes folder structure Dec. 2011 - https://discussions.apple.com/thread/3547807?answerId=16923545022#16923545022
see also:
Image of folder structure and explanation of different iTunes versions (turingtest2 post) - https://discussions.apple.com/thread/2741246?answerId=13025536022#13025536022 and https://discussions.apple.com/thread/3700206?answerId=17457605022#17457605022
If you want your full library listing back then you will have to recover it from your bakup drive (which is why you have it). Alternatively you can create a brand new library file, add the media to it, and start new.