Hello,
IT PRO here.....
Now to get this straight here you did test the HDMI port... fan and everything comes on..
It sounds like the LCD itself is dysfunctional. Which is the screen on the actual lid of the laptop.
The HDMI cable you plugged into the laptop ties into graphics card which bypasses the screen itself all together.
It seems like you will be in need of a replacement LCD.
Let us know if the battery unplugging worked otherwise you will have to replace the screen.