How can I deauthorize iTunes on all computers?

“I got a new computer, installed iTunes, and now it says I can’t authorize my computer because I have too many. This is the only computer I use so how can I deauthorize iTunes on all computers I’m not using?”
Part of the deal Apple made with music and movie companies when they started selling songs through iTunes was to limit the number of computers where the stuff could be played. This translates to times where you won’t be able to access your iTunes purchases like what happened to you here. Fortunately you can deauthorize previous computers, Apple just doesn’t make it obvious how to do it.

If you hit the maximum of 5 authorizations allowed by iTunes, you can reset your authorization count by clicking Deauthorize All in the Account Information screen. You can’t actually see this feature unless you have maxed out the number of authorizations.
To access this feature, open iTunes and click the iTunes Store in the menu on the left side of iTunes. If you’re not currently signed in to your iTunes Account, click the Account button and enter your account name and password.
Click the Account button again enter your password and then click View Account.
In the Account Information window, click Deauthorize All.
Deauthorize all iTunes computers
This feature is only available once every 12 months. The option will not appear if you have used this option within the last 12 months. If you need assistance because you can’t get the deauthorize to work, click the support link in iTunes and contact support for further assistance.