The only other thing I can think of is running it till the battery is dead and then pressing the power button for 10-15 seconds to remove any discharge. Then plug the power cord back in and give it a few minutes before pushing the power button to boot it up.
Hopefully it isn't fully charged as I know you have no way that I can think of to determine when/if the battery is fully discharged? I used to work at Staples and I would see laptops from time to time that were dead and removing the battery and power cord, then pressing the power button did the trick needed.
But I have no idea how you can drain it or know when it is drained!
Sorry for not getting back to this thread to let everyone know what's going on.
We took the Surface Pro 3 to a Microsoft Store. It turns out that it had to do with a Windows 10 update/upgrade. He managed to get it booted somehow and downloaded some application from the Microsoft website that solved the problem. Apparently the application stops the update and runs it in a different way which resolves the problem. I'm sorry I can't find the application, or remember what it was called. If I do find out, I'll post here with a link.