Just slide and hold the power button for 20 seconds. This should reset the firmware.
To reset the battery, plug your Kindle into the charger for 30 minutes. After that AND WHILE STILL PLUGGED IN to the charger, slide and hold the power button for 30 seconds. Then see if it begins charging. If not, let me know the approximate purchase date.
Ah....the batteries normally last 2-3 years. I would replace it. You can find a replacement at the below link: