Here is how I got my surface pro 3 to finally turn on.
I used Two-button shutdown procedure below:
Don’t use this process on Surface RT or Surface 2.
Use this two-button shutdown process to ensure that Surface is turned off completely.
Step 1: Swipe in from the right edge of the screen, and tap or click Settings, tap or click Power, and then tap or click Shut down to shut down Surface.
If you can’t shut down Surface normally, press and hold the power button on your Surface for 10 seconds.
Step 2: After Surface turns off, 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.
Step 3: After you release the buttons, wait 10 seconds.
Step 4: Press and release the power button on your Surface to turn it back on.
If your Surface still won’t turn on, it needs service. To request service, see Surface Online Service Center.