I am shortly going to be reformatting a Windows computer that my wife uses for iTunes. She keeps her library and her library files on an external drive. This is her active library -- that is, it is NOT a backup. (She does not have any files on the local hard drive, and always launches iTunes holding down the Shift key so that she can choose her library from the external drive.) Her external drive is currently not available, however. Can we deauthorize the computer from her account JUST by logging her into the iTunes store from that computer and deauthorizing it? Or does the external drive with her library need to be connected before we can deauthorize the computer?
The authorization link is between the computer and the Apple ID, not any particular iTunes Library. So, no, you don't need the library to break that connection. You can create an empty library temporarily, just to get iTunes to launch, then use Deauthorize This Computer.
If you throw that computer in the garbage, you can always go to your iTunes account on another computer and click "Deauthorize All" to remove all authorizations at once. You can then reauthorize your current computers as needed.