Just had this happen with Windows 8.1 Surface Pro 3:
1. Symptoms:
Power Adapter. Pay close attention to power adapter connection on SP3. When you press the power button it flashes for a second, every time This is the key symptom that separates it from the typical black screen.
Black screen.
Resolution: None of the typical combination button fixes worked Hold the power and up volume etc... Here is the fix that worked. Connect the power charger as normal, connect an external USB power charger to the USB Port, hit the power button and it started up. The key fix combination of the SP3 power supply and an external power source started the system after five hours Troubleshooting and trying every fix on the internet.
I do agree with some of the blogs it has to involve a protective circuit in the SP3, the user mentioned the system stopped responding, here are two key clues: When I got the system to turn on the battery was fully charged and the time was stopped at the time of the shutdown three days prior to my getting the system to turn on