f the battery isn’t too far gone, here’s how to revive it:
Owners of the Kindle Fire HD have commented on numerous problems with the battery and charging. Some simply refuse to charge, whereas others will charge only a fraction, and charge very slowly.
Plug the device into the Kindle A/C adapter (not your computer) and let it charge for a few hours.
Be sure the charging light is lit — sometimes a drained Kindle will stop charging a few seconds after you plug it in.
Unplug and replug until the light stays on steadily, then leave it alone. Most of the time you’ll come back to a restored Kindle. If not, go on to step 2.
If you still see the same Critical Battery screen after charging, unplug the USB cord, then hold the power slide to the right for at least 20 seconds.
Click here: Kindle fire Technical Support