Amazing, I have the exact same problem. Just downloaded a book from Overdrive, and I've got the file on my computer but the software will not regonize my Nook.
The computer does recognized it, and both the Computer and the Tablet are authorized. I've reset the Nook and the computer a few times to try to get it to click but nothing happens.
There are various DRM eBook apps that should work on the Nook.
Register it with the same Adobe ID as you use on the laptop.
Copy books from the laptop with the Nook plugged in, using a file manager such as Windows Explorer or Finder.
You should then be able to read them on the Nook.
I'm not sure if the Nook comes with an Adobe DRM capable eReader app builtin.
Also not sure if any of the apps will integrate with ADE to allow copying direct from ADE (as with a dedicated eReader) rather than using file manager.
For Overdrive library books, you can install the Overdrive app on the Nook.
That should allow you to borrow, download and read library books on the Nook without using PC/Mac/ADE at all.