If your Surface Pro won’t turn back on after shutting it down or restarting please try the following steps from Microsoft:

These steps are assuming that your Surface Pro is charged..

Step 1

Press and hold the power button on your Surface for 30 seconds and then release it.

Step 2

Press and hold the volume-up button and the power button 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.

Step 3

After you release the buttons, wait 10 seconds.

Step 4

Press and release the power button to turn your Surface back on.