Surface Pro 3 Black Screen
1.Click "Widowsbutton" + 3 times "P" 

Reference video: https://www.youtube.com/watch?v=2AEjjzhMa70

2.(1)Attach the power supply(2)Wait twenty seconds(3)Press and hold the power button for 30-40 seconds and then release(3)Turn Surface back on

Reference video: https://www.youtube.com/watch?v=b6KfZ0x9xbM

3.Press and hold the volume-up button and the power button on your Surface at the same time for at least 15 seconds, and then release both.The screen may flash the Surface logo, but continue holding the buttons down for at least 15 seconds.
After you release the buttons, wait 10 seconds.(Note:If you have access to Bios, select Exit Setup and choose Yes)

Reference video: https://www.youtube.com/watch?v=w5Q7zLXAM64

4.Connector loose? Battery depleted? Power adapter broken? Check battery or power adapter or google "Surface won't turn on, Windows won't start" to find solutions by Microsoft.
QQ
WhatsApp +86 13828829556