Please reset the kindle by holding down the on/off switch for 40 seconds (use a watch to time) ignore any messages the kindle may display, then release your finger the kindle should reboot and re-load the operating system, you may have to do this both on and off the charger and upto 4 times before it resets. Charging issues are usually caused by the kindles software going bad.
Let me know if you need more help
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I understand however its not just the power-button being pressed you need to follow what I indicated above please by holding down the button for 40 seconds as I have indicated this resets the kindle, the screen will flicker and should fire up further charging issues should be resolved
OK so you are holding the button down for 40 seconds then releasing your finger there is no response from the kindle both on and off the charger is that correct please?