You must use your original Adobe account to real books bought and downloaded while using that account.
I'm a but confused by I tried to authorize Adobe digital edition in my new Tablet, ADE does not run on any tablet except a full Windows 8 tablet.
What id you try to authorize? (1) ADE running on a Windows 8 tablet, (2) an app running on a normal tablet, or (3) ADE itselft running on a computer.
In any case, you must deauthorize the new ID, and then reauthorize with your original ID.
On ADE, the deauthorization is ctrl-shift-D (cmd-shift-D on Mac). If you can't reauthorize with your original ID, post detailks and the message you get when trying.
For a tablet app, see help for that app for deauthorization/reauthorization.