I recently purchased a new computer. I downloaded Digital Editions 2.0, authorized it with my Adobe ID, then downloaded books from my library. All of this works fine.
When I try to transfer the books to my Nook (previously authorized with our old computer and same Adobe ID) it says No Permission to copy this book. I have tried returning the books and rechecking out etc. and can't transfer anything but the manual to my Nook now.
It sounds as if authorization on your Nook is confused.
While it is plugged into the computer, and ADE running in library mode, deauthorize the Nook with ctrl-alt-E (cmd-alt-E on Mac) and answer any prompts.
Restart ADE, and reauthorize the Nook (menu~Help~Authorize Device)
If that doesn't work, you may have hit a device that ADE2.0 doesn't support properly.
There are lots of bugs in ADE2.0. Try replacing ADE2.0 with the older but more reliable v1.7.2.
(You can have them both installed at once if you like.)
Version 1.7.2, it is a little difficult to find, available on Adobe site for Windows and for Mac.
The forum software is sometimes corrupting the link above. There shouldn't be a blank in 'editio ns.html'. The following redirects to the same page: http://tinyurl.com/diged172