Almost certainly the transfer of the program without reactivation has confused ADE.
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 had the same problem. The solution that worked for me was to find the activation.dat file in the Library/Application Support/Adobe/Digital Editions folder and drag it to the Trash. Then I was able to deauthorize the computer in ADE (either Help>Erase Authorization or Command-Shift-D while ADE is open) and reauthorize computer ( Help>Erase Authorize Computer).
General comment to Adobe: Your customers do change computers. EVERY Adobe program (Lightroom CC, Photoshop CC and ADE) was a PITA to bring up on the new machine. Adobe is the worst; almost all other programs came up with little or no problem.