Yes, I just went through this with my 1st gen Paperwhite - I wanted to transfer it to my daughter from my son.
Short version : you can't register it anymore - Amazon doesn't support it for registration any longer.
This Verge article perfectly describes the situation, even though it talks about different devices.
Long version : I was furious! Still am. I scolded many reps over the course of 2+ hours troubleshooting this when they broke the news : why on earth would Amazon let people deregister if they can't register again?? Why aren't they emailing customers about this - they notified us about not being able to use the store any longer! They said I had to buy a new device, which I did. I told them they should reimburse me that cost...they offered me 50%. I threatened to sue them in small claims court (US) and they agreed to reimburse me 100% of the cost of a new one.
And yes, I surely would have sued them for the $150+ cost, no lie.
This feels like a good reason that lawyers and class action lawsuits exist.