iTunes does pretty much everything through the Library file (sometimes ending with .itl). A copy of the file ending in .xml is usually located in the same folder. It is the library file that tells iTunes where you music is located, what playlists exist and their contents, song ratings, etc. Without it your files are just a series of media files. If you previously had iTunes set to keep just media on your external drive then the library file was located on the internal drive of your old computer and was lost along with everything else, including possibly some artwork. Your only resort now is to make a new library and add the files to it and start again.
If I am mistaken and in fact you had your whole iTunes collection (the whole iTunes folder and everything it contains) on the external then the correct way to open the old library is to hold down the option key while starting iTunes.
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
iTunes: How to re-create your iTunes library and playlists - http://support.apple.com/kb/ht1451