When iTunes starts it looks for 'iTunes library.itl' That file tells iTunes it what's in your playlists, where your media files are located and where each track should go to play a media file, etc. The .itl file is central to iTunes. If it cannot find one in the default location, or the last location where you normally keep one, you get that message. Sometimes you get it if you deleted the iTunes folder on your internal drive and just keep it on the external drive but the external drive is not mounted on the computer in when you start iTunes. I don't see one on your external drive, nor any of the other files and folders that normally accompany it, so maybe you normally use this drive with another computer and that file and those folders are on that drive.
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
Where are my iTunes files located? - http://support.apple.com/kb/ht1391
If that other drive was one of your office Macs and you cannot retrieve it you will have to make a brand new library. this time put the whole library on the external drive. Start iTunes with the option key held down and have it create a new library on the external drive. Drag the items in the media folder to the Automatically Add To iTunes folder in the new iTunes folder. This will add them to the library and move the files to the correct location. You will need to make sure the external drive is always turned on before starting iTunes or you will have to hold down the option key while starting iTunes and point it to the .itl file in your new library so it knows where to start.
