Which version of Adobe Digital Editions are you using? Are you positive the user account activated in ADE is the same account you have been activating on the Nook? Finally which e-book provider are you using to purchase the book from?
I'm using ADE 2.0 and yes I'm positive that its the same account on both my computer and my nook I unauthorized and reaithorized both devices several times. I've gotten the books from livebrary am online library site.
Thank you for the update cmcgrath0894. You can verify the account being utilized in ADE 2.0 by going to Help>Authorization Information. If you have already verified the accounts are the same then I would recommend contacting the e-book provider and request they reset the activation information on the books you are borrowing. You will then want to download the books to ADE and transfer them to the Nook using the process discussed in Transfer eBook to eReader | Adobe Digital Editions - http://helpx.adobe.com/digital-editions/kb/transfer-ebook-ereader-digital-editions.html.
I just happened to come across a similar problem with my mother's new Nook HD for her books she checks out through the library. HOWEVER, we did find that B&N has available through their site free apps for both libraries that use Overdrive Media Console as well as libraries that use the 3M Cloud Library. All you need to do is download these free apps to be able to directly download from your library's site into your Nook.
Overdrive Media Console: http://www.barnesandnoble.com/w/overdrive-media-console-overdrive-inc/1113021293
3M Cloud Library: http://www.barnesandnoble.com/w/3m-cloud-library-3m-company/1113021300
Once you have downloaded the correct app for your local library you can access the app in with all of your other apps. Within the app it's self is where you can find your library books. My mother was so excited to find out we could do this. She is good with a computer but it takes her a few times to learn how to do the file transfers/drag&drop so for a direct download to be available is a really big relief to her not having to learn something new and complicated.
After looking at the Live-brary site, it is powered by Overdrive Media Console, so you will need that app on your Nook. Though I don't know that these apps work for other sites not powered by one of these consoles, so anything bought from another site may still need to be downloaded into ADE and then using drag&drop or copy&paste, then transfered into your Nook's book folder.
Hope this helps you out and wishing you the best.
@cmcgrath0894 Is it a Nook eReader or a Nook tablet?
If it's an eReader, there may be a compatibility issue with ADE 2.0.
Try uninstalling it, and installing v1.7.2 instead.
Version 1.7.2 is a little difficult to find,
available on Adobe site for Windows and for Mac.
If it's a tablet, you will probably need to install an appropriate eReader app,
such as Bluefire (which will work for most/all books ADE will handle), or one of the apps in the previous post.
I don't think ADE will transfer directly to these devices, but as long as you register the app with the same AdobeID on PC/Mac and tablet,
you can copy the files then read them from Bluefire.