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This usually happens if the firmware/software is glitched. First we can soft-reset the tablet and see if it works or not. Press and hold down (or slide) the Power button for full 40 seconds and this will reset the Kindle.
If that didn't work, then you can try de-registering the Kindle and re-registering it with your Amazon account. Go to Settings> device and/or Registration and de-register from there. Then re-register it from the same menu. That should fix it
(After registering, you will have to download all your books using your same Amazon account you used on it)
Please let me know if that didn't work, so we can continue troubleshooting