iTunes: How to move [or copy] your music to a new computer [or another drive] - http://support.apple.com/kb/HT4527
Quick answer if you let iTunes manage your music: Copy the entire iTunes folder (and in doing so all its subfolders and files) intact to the other drive. Start iTunes with the option (shift on Windows) key held down and guide it to the new location of the library.
do not confuse moving your whole folder and library with moving just media files as in
iTunes for Mac: Moving your iTunes Media folder - http://support.apple.com/kb/HT1449
The library.itl file is the central controlling file of iTunes. It contains the file locations. When you open this library it displays your content (as it know it) and playlists, etc. When you play a track it checks the file location in iTunes and goes and plays that file. If the file is not where iTunes thinks it is, you get a broken link.
You didn't change your library location. What you did was tell iTunes, in future, to put all media in a new location. Did it ask to move your old media, and did you say yes? If it didn't move it then you may end up with split media. Existing media is still where you put it (as seems to be the case from your description), new media will go on the external.
In general the above is not what most people want to do. To correctly move the "library" (I say collection so as to not confuse this with the library file) you want to drag the whole iTunes folder to the external and tell iTunes when it starts up where the new location is. This is assuming you have everything in a nice, neat package in that folder. Now if you're in an intermediate stage then things are messy, but you'll have to let us know where you various files are at this stage.
Some people only want to move their media. That's okay, but you have to know what iTunes is doing, and also realize it gets tricky when moving the collection in the future.
OK, I moved the collection. It is all nice and neat/organized. Really i am just going from one external HD connected via my airport to an external HD conenected via firewire.
Everything is copied over.... just need to make sure iTunes knows where the collection is. I have done this before... but i guess I forgot.
I am the developer of an application called TuneSpan. It may be able to help you manage your library in a different way.
With TuneSpan you can keep your default media location the same, so new music get added to your internal drive, but you can move any media wherever you choose. Through TuneSpan you can select any media type, playlist, artist, album, tracks, etc, etc, and just select a location to move the files to. TuneSpan will copy the files, set the locations in iTunes, and clean up after itself, trashing original files and empty folders as well so your system stays clean.
TuneSpan is available on the Mac App Store, and you can check it out at http://tunespan.com
I hope TuneSpan can help you take better control of your iTunes media.
I may receive some form of compensation, financial or otherwise, from my recommendation or link. <Edited by Host>