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The problem you're having is often due to the software in the Kindle locking up and it needing to be rebooted. To do this, simply press and hold the power button on the Kindle for 40 FULL seconds, then release and wait a full minute for it to reboot (do no press anything else within that minute). If this does not cure the issue, try that reset up to THREE TIMES and wait the full minute to see if it reboots.
If you're still running into problems, then try plugging the Kindle into the charger for 15 minutes, then eject it and try the reboot a couple of more times.
If the device still does not work beyond that, then this would indicate a hardware fault in the Kindle requiring repairs.
In the latter case it's generally not cost effective to repair a 10 year old Kindle (as the cost can encroach what a new replacement one costs). In that case I would suggest replacement versus repairs. Once a new Kindle is purchased and registered to your Amazon account, your books and content will "Sync" to the new device (so none of your books are lost). You can view the various model Kindles at the link below if you'd like:
Other than that, I'm sorry for the bad news here and wish there were a quick fix.
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Please view my reply for the answer to your question.