A colleague who shall go unnamed is in the process or moving and has unearthed what he believes to be tainted treasure. He writes:
I have a really old iBook that’s still running 10.2.8 and iTunes 4. I am trying to deauthorize this computer, but when I try, it says that it can’t connect to the iTunes Store. (Got it plugged into Ethernet, so Internet connectivity isn’t the issue.) Please tell me I don’t have to upgrade iTunes just to turn off this account on this computer.
You don’t have to upgrade iTunes just to turn off this account on this computer.
Oh, you wanted more than that? Very well. This can be filed among several similar “I have/inherited/know about Computer X that is authorized with my Apple ID and I’m unable to deauthorize it” conundrums that routinely scoot across my desk.
It’s generally considered bad form when playing a board game to grab the aforementioned board and throw it and its accompanying pieces into the air. However, in this case, I heartily recommend it. And by that I mean rather than spending hours trying to elevate this computer to a state where it and the iTunes Store see eye-to-eye, you’re better off starting over. And by that I mean resetting all your authorizations and then reauthorizing just those computers that you currently use.
This is easily done. On the computer you currently use launch iTunes. You will see your Apple ID in the top-right of this window—email@example.com, for instance. Click on your ID and in the resulting dialog box, enter your iTunes password and click the View Account button.
In the Account Information pane that appears, seek out the Computer Authorizations area. Here you’ll find the number of computers that are authorized to use your Apple ID—your ancient iBook is one of them. Next to this entry is a Deauthorize All button. Click it to do exactly what it says. All your computers will be deauthorized.
At one time this button didn’t become visible until you’d used all five of your allowed authorizations. This is no longer the case. However, you're still limited to deauthorizing all of your computers to just once a year. If you do it today, you must wait a year before you're allowed to do it again.
Now, as needed, authorize the computers you currently use by choosing Store -> Authorize computer.
Update: Corrected suggestion that you can deauthorize more than once a year. That is not the case.