Hi I have a Surface Book and had this happen a few times.
Two things have worked for me.
1 If the screen will detach detach it and put it back and try powering on.
2 Try a 2 button reset. See below. The up volume on the volume button is the +
To perform a two button reset on your Surface Pro 4, do the following:
- Press and hold the power button for 30 seconds.
- After Surface turns off, press and hold volume-up button and the powerbutton at the same time, for at least 15 seconds (The screen may flash the Surface logo before 15 seconds, but don’t release the buttons).
- After you release the buttons, wait for 10 seconds.
- Press and release the power button again, and your Surface will be turned on again.
Hope this helps.