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Remove any cover that is on the kindle, then locate the power switch on the side, then Plug the Kindle into the charger for 3 minutes. After 3 minutes and while still plugged in, slide and hold the switch for one minute. Allow 3 minutes afterward for the Kindle to reboot. If this doesn't correct the problem, let me know the approximate purchase date of your Kindle.
you can try holding the power button in for 60 seconds then try charging for 5 minutes, repeat he process a few times. Also try connecting to a computer and press and hold the power button while connecting and reconnecting the usb cable to the computer.(insert the usb and remove it a few times while holding the power button on the kindle)