It does sound like a bad display and that is not economically feasible to repair however please try this>>
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.
Let me know if you need more help
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How is this working out please?
Is this working now please?