You need to unregister the ID on the new computer, using ctrl-shift-D (cmd-shift-D if a Mac) and follow the prompts to confirm.
Restart ADE, and you should be able to register with your old ID and access your books.
Probably what went wrong in the first place was a confused registration:
ADE often gets its registration/activation confused and in a semi-authorized 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 (which is probably why you were misled into trying a new ID).
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.
