Open ADE, go to 'help' and then 'authorization information' (paraphrasing since my copy is German).
There you should be told, that your computer is already authorized. You should also see the Aobe-ID it is authorized with.
If this information is as you expect it to be, everything is fine. Books you download with this version of ADE will be encoded with your Adobe-ID. Every device authorized with the same Adobe-ID will be able to read these books.
ADE on a computer can download book also if it is not authorized. It uses then some internal number that is unique to this installation instead of the Adobe-ID. Books downloaded with an un-authorized version of ADE can only be read in that version of the software. Alf could still help you as long as you use the tools on that computer.
There is a keyboard short cut for unregistering ADE on a computer. I don't know it right now, but google should be able to help.
If the Adobe-ID your ADE version on your computer is authorized with is not the one you want, you should un-register the software and re-register it with the correct Adobe-ID.
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