If none of the previous solutions works (the most important troubleshooting steps), I have good and bad news for you (please don't shoot the messenger).
Bad news is that your Kindle is defective. I have provided you with the all troubleshooting steps for resolving this kind of issue (resetting the software, force reset). Unfortunately there is an hardware issue on the device that software troubleshooting can't resolve.
The good news is that Amazon does often replace Kindles out of warranty. At least they would replace it for less than the cost of repairing.
You will have to contact Amazon warranty support service at 1-866-321-8851 to arrange replacement.
There is an option that Amazon calls you. Please follow the steps below:
1. Go to the page below - click here
Log in using your Amazon account information.
2. Select Kindle > Kindle Device (or Troubleshooting my Kindle) > Problem with my Kindle > My Kindle is damaged or Kindle is frozen/unresponsive
3. Click Phone - Call us
4. Enter your number and choice "Call me now" or "Call me for 5 minutes".
Sorry I could not be of any more assistance, but there is no more options we can try online.If you are not satisfied with my personal service (my effort to help) or you need more information please do not rate my answer negative BAD service or POOR service that will result in a permanent negative feedback on my record (very damaging for me). Reply to me using "Reply to Expert" button (just reply "I'm not satisfied") and I'll connect you with our refund office (your deposit will be refunded).