Sounds like you have tried everything you can.
I have a normal paperwhite and every three months or so it refuses to turn on. As Haz says you need to hold down the power button for at least 30 seconds (longer in my experience) until the sucker boots. If that fails then I would guess that the thing isnβt charging properly and the battery is dead. With a totally dead battery, it takes at least an hour to get sufficient charge to come back to life. But if itβs not charging then itβs likely buggered properly.
Whilst charging there should be a small green light shining. If that isnβt lit then maybe try a different usb cable.