Can't authorize my Kindle in ADE

I'm trying to authorize my Kindle by plugging it into my pc, while ADE is open. My goal is to send the book from ADE to my Kindle, as my library FAQ tells me to.

But the "Authorize computer" is grey, and the Authorization Info just says "This computer is already authorized".

Also, your support says they can't "locate any active subscription under this account". I don't know what that means. And if I don't have an active account. how come I can open libabry books in ADE?