Please follow the steps below:
1. Press and hold (or slide and hold) the power button on the bottom of the device for 30 seconds.
2. After the 30 seconds, release the power button.
3. Wait 2 minute, then turn on your Kindle.
4. Then try to recharge your Kindle.
If the previous procedure doesn't work, please try this:
1. Plug the Kindle into the charger for 10 minutes.
2. After 10 minutes (while still plugged in) press and hold power button for 20 seconds.
3. Allow up to 3 minutes for the Kindle to reboot.