MacBook Pro blank display even on external monitor

Open the bottom case. Disconnect the battery. Disconnect the on-board video and apply a bit of tape over the connector to avoid shorting it out. Reconnect the battery. Put the bottom case back on (though don't screw it in place yet). Connect the computer to an external display using whatever adapter(s) necessary. Plug in AC power. Turn on the computer.

Does it boot and do you get an image on the external display?

If yes, you have a bad screen.

If no, more troubleshooting is required. Disconnecting power (AC and battery) before every step, try disconnecting single components and repeating the experiment until you get a display; track pad, top housing, speakers, SSD, etc. If it comes to life after disconnecting one of those, then you have a bad whatever-the-last-thing-you-disconnected. If it still doesn't come to life, you have a bad logic board.