Your Amazon Fire tablet's power on/off button can be stuck. Even when you're pressing it, the external power button could not be responding to your push.
The screen of the gadget is broken.
The battery on the Amazon Fire tablet is completely dead. It lacks the required battery power to turn the device on.

The Amazon Fire HD tablet's battery has to be replaced because it is dead.
It's possible that a third-party programme damaged the Amazon Fire tablet's Amazon Fire OS.
Damage to the internal hardware that you are unable to repair.
Firmware issue with the Amazon Fire that requires professional advice from Amazon. These could be reason for why won't my fire tablet turn on.