Do you still have this problem? I found a video somewhere on youtube that shows how to at least turn your laptop on and backup all the data you need. Me myself have been living with this kind of solution from late 2017.
So my HDMI port is not usable anymore, repair shop assuming it's my graphic card that cause this problem. The keyboard backlight works fine, the capslock button works fine. All that happens is the laptop screen is not showing anything after the macbook chime sound heard.
The step is turn your macbook and make sure the keyboard backlight is on. Put your laptop on couch or bed (any soft surface to cover all the hole on the backside of the laptop). I usually cover MacBook with blanket or jacket. Do this for about 30 second and then open your laptop, if the screen is not on yet repeat the step.
Sometime it takes up to 10 times to open and cover your laptop again with jacket. If you think it's not working after a lot of retries then turn off your mac by holding down the power button. You can turn it on again and retry the method above
People said that this trigger your graphic card selection caused by the sensor that detect the heat of your mac (since we covered all the holes with blanket / jacket / put it on soft surface such as bed). How? After you put your macbook on, the fan will always start rotating. The moment when you block the air that are flowing it will cause the temperature to rise and the macbook choose the other graphic card that are working.
Hope this helps.