If you do need to de-authorize, then ctrl-shift-D (cmd-shift-D on Mac).
BUT ... You can have up to 6 devices authorized at the same time with the same Adobe ID/account.
You may have been confused by a stupid and completely misleading ADE error message.
Sometimes ADE gets its registration/activation confused and in a semi-authorized state.
Uninstalling and reinstalling does not help, and indeed installation can even trigger this state.
Unfortunately, it often then gives misleading error messages about what is wrong.
A common incorrect message informs you that the ID is already in use on another computer and cannot be reused.
Another is "E_AUTH_NOT_READY"
This can often be resolved by completely removing any authorization using ctrl-shift-D to the Library screen on ADE (cmd-shift-D if on Mac).
Restart ADE, and then reauthorize with your (old) Adobe ID.
In extreme cases on the mac, the following extra step has helped some people. Navigate to /Users//Library/Application Support/Adobe/Digital Editions and drag the activation.dat file to the trash. If you are using 10.7, see Access hidden user library files | Mac OS 10.7 Lion. http://forums.adobe.com/thread/1265248?tstart=0
Thanks for your reply.
My question was misleading or incomplete. My old computer, a PC, is no longer working. When I installed ADE on my new PC, I received the error message re authorization already in use (or words to that effect.).
OK good. The solution above is probably the right one for you, then.
Post back if you still have issues after that.