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This is usually an issue with the Firmware, so I would first like you to do this please.
Remove the charger from the Kindle and hold the power button to off for 35 seconds.
Release, then connect the charger and try to turn on the Kindle.
Let me know the results please
ok, you will need to reset it then, then set it up
Enter the pin
Or if this is rejected
And choose to reset it
If it does not accept either, keep entering the wrong Pin until it asks if you want to reset it and choose to do this (a Factory Reset)
Once done, you can set up the Kindle again
Let me know please how you go