You need to make sure your new copy of ADE (Digital Editions) is registered with exactly the same Adobe ID as your old one was.
DRM books are locked to a particular Adobe ID.
Authorize it (ctrl-shift-u, or menu/Help/Authorize Computer).
If that doesn't work, try deauthorizing and reauthorizing as below.
Sometimes ADE gets its registration/activation confused and in a semi-authorized state.
Uninstalling and reinstalling does not help.
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.
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
I've tried the reauthorization on ADE 2, plus downloaded ADE 1.7.2, and still got the same result. I also get the message E_GOOGLE_DEVICE_LIMIT-REACHED when trying to download an ebook I bought via Google that I could previously open.
There is a maximum of 6 devices that can be registered to an Adobe DRM ID at a time.
Try Adobe Live Chat: http://www.adobe.com/support/chat/ivrchat.html
They can reset your authorizations, and then you must reauthorize any devices you still need.
(Unfortunately, Adobe haven’t got round to an admin website for viewing and editing authorizations.)
Some of the representatives haven't been properly trained and don't know what to do (and claim there is nothing they can do);
in that case the only way seems to be to give up that chat and try another session hoping for a properly trained representative.
If your problem is with another device using Overdrive, Bluefire, Aldiko or similar third party app, it is recommended not to mention that app when on the chat, just mention that you have run out of authorizations (E_ACT_TOO_MANY_ACTIVATIONS) . Thanks to AJP_Bear for that tip.