It sounds like the headphones you are using are broken. Try using a different pair of headphones. If the problem persists with new headphones, jiggle the plug around the headphone jack. If you can hear sound or static, the headphone jack is most likely the problem and will need to be replaced. For more information, check out our troubleshooting guide.
First, make sure that the Kindle Fire is charged. To check that it is charging, make sure the charger is plugged into your device correctly, and that the outlet you are using is providing electricity. (Try plugging in something else to the same outlet and making sure that it works.) If your device is charged, but still not powering on, there is most likely an issue with the motherboard. There is an even higher likelihood that your motherboard may have failed if your device has been subjected to any water damage or a powerful electric shock. For more information, visit our troubleshooting guide.