The TV is possibly being controlled through the HDMI-CEC standard. It can be disabled on the Fire TV device under Settings -> Display & Sounds -> HDMI CEC controls.
I would reseat the ribbon cables closest to the battery. As seen in the guide for battery replacement for this device. Such connectors should be accessible once the back cover is taken off.
This happened with my iPod touch 7th Gen, i thought the LCD broke too. Waited for it to discharge then it booted up normally after. If that does not work, replace the display (or have it replaced)