As noted in the comment by m.goodwin24, the micro-USB port can be faulty. If you have extremely good soldering skills, this is something you can fix. It just requires removing the case and resoldering the pins on the port. But note that the pins are very small and close together, so this requires a fine-tip soldering iron and good skill to work on.
To verify whether you have this problem or not, you can try a couple of things. One is to use the USB cable to plug the Fire TV into a computer. If the computer doesn’t recognize that any device has been plugged in, you may have this problem. You can also use a USB port power measuring device which you plug in between the power adapter and the Fire TV. If it shows 0 mA current draw, then you probably also have this problem.