"I have had the same issue for 2 years with my Surface 2 purchased in 2013.
when I press the power button, the screen does not start (stays black)the windows button works (ie it vibrates when pressed)the power cable’s light is on for approx. 10 min and then goes offWhen I hard reboot, the windows button does not vibrate anymore
I managed to start it again by hard rebooting then pressing the power button many many times. At some point, it starts, and when it does, I keep it turned ON all the time (no sleep, no hibernate, no power off - see power options).
I don’t know how to fix it. I feel it is the battery because the time goes off after such restart. Battery should keep it but it does not, so that’s my clue.