If your Kindle Fire won’t turn on, you can try disconnecting the charger, hold the power button for 30 seconds and then pressing power button again. This usually gets it to turn on.
Another problem you may face in the kindle fire is your computer not recognizing your Kindle. You could fix that by un-installing the drivers and then re-installing the driver. That should get the PC to recognize the Kindle Fire. You can reference
Another issue users reported is the sleep of death after rooting in which the screen doesn’t come back on after it goes to sleep. This is usually caused by Wi-Fi still being turned on when screen shuts off. An app called Auto Airplane Mode automatically turns off your Wifi when your Kindle screen goes blank. This App will prevent you from getting the screen of death on your Kindle Fire or Fire HD.
If your Kindle Fire or Fire HD is not charging. 70% of the time the issue is caused by a bad charging Chord. Get a new one and it will most likely start charging your Kindle just fine.