You need Digital Editions (ADE) and the Nook to be authorized with the same AdobeID.
From ADE with the nook connnected, choose menu/Help/Authorize Device.
That will copy the authorization from ADE onto the Nook.
You should then be able to copy.
If you haven't got an AdobeID, visit http://www.adobe.com/ , try to sign in, choose the 'no Adobe ID' option and it will allow you to create one.
If you have not authorized ADE with any AdobeID, it will have made an implicit/anonymous ID.
That can't be used for transferring books to another device.
In that case
Borrow books again. They will now be associated with your AdobeID and should be able to be copied to the Nook.