@Tinut Just checking ... when you installed ADE on the second computer, you did use the same Adobe ID that you had used on the first? And so you didn't need to change the authorization on the Kobo?
What has probably happened is that the authrization on the old computer got confused.
That can happen when you uninstall and reinstall ~~~ it half remembers the old registration,
not enough to read books and transfer properly, but enough to claim to be authorized and to refuse to accept new authorizations.
Try completely deauthorizing and reauthorizing as below ...
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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