Try resetting the firmware by pressing and holding the power button for 20 seconds. Let me know if it still doesn't respond.
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.
The batteries last 2-3 years. I would replace it. You can find a replacement at this link. https://www.amazon.com/Replacement-NOOK-BNRV100-Installation-Extended/dp/B00GTLXVL4/ref=as_sl_pc_ss_til?tag=thcosezo-20&linkCode=w01&linkId=EHC3BKGOBCFO32DD&creativeASIN=B00GTLXVL4
They may not have it. Keep that link for future reference. Have a wonderful week.