Sorry to say this, but: it was Amazon's own decision to make debricking the Paperwhites essentially impossible for the end user. So nobody here can give you an advice that doesn't require opening the device and soldering.
Except for this one: Plug the Kindle to a wall charger, and let it sit there for at least 24 hours (and then possibly force a reboot by pressing the power button for about 20 seconds). I doubt that it will work, but you have nothing to lose, so give it a try. Dead batteries cause a lot of different issues, and maybe (hopefully) yours is one of them.
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