Also be sure to check the email connected with your Amazon account after a registration attempt for an email from Amazon. Sometimes you will get the registration error message and have an Amazon email with a special passcode number that you need to use one time to register your device in place of your normal password.
I wouldn't spend too much more time on this. If it is new and still under warranty you should be able to get support to send a replacement.
Have you talked to Customer Service yet? They are the only people that can help with a persistent failure like this, since it usually requires access to Amazon's servers which nobody in this forum has.