Try a deeper reset. Plug the Kindle into the charger for 30 minutes. After that AND WHILE STILL PLUGGED IN, press or slide and hold the power button for 30 seconds. After that, try using it. Let me know the approximate purchase date if it still fails to function.
It may be the battery. They last 2-3 years on average. If you can provide the tiny model number on the back, I can find the battery you will need.