I was in the same position - old computer crashed after two weeks when I upgraded to Windows 10 - hardware probably incompatible or old. My boot disc wouldn't recover it so I had to buy new one with preloaded Windows 10.
Got red error msg about not being able to use previous e-mail ID for authorisation. I saw this tip on an Internet page when I researched it.
Open Adobe Digital Editions - then Type in Crtl+Shift+|Del.
I can't understand the logic but it worked for me - I was then able to type in my usual e-mail address and it was authorised and it is working OK for new books I am downloading from my local library and they transfer to my Nook reader OK.
The only snag - it wouldn't work for one I had just downloaded previous to authorising it. I will have to read that one in my browser. Shame!