Alright, I think I know what happened. My friend gave me this Kindle because it had a broken screen (if I could fix that, it was mine to keep). I ordered a replacement screen, fixed it,
reset to factory settings without unregistering it first 
, and a few days later I tried to register it to my account. Since Amazon still had it listed under my friend's account, they assumed it was stolen and blacklisted it.
By the time we realized I couldn't register, and my friend unregistered it through the Amazon website, it was too late. We'll have to write to Amazon and see if we can clear things up.