Ok, so I had a similar issue. My Surface Pro 3 wouldn't turn on no matter what button presses I did. I looked through a bunch of forums and did everything they said but to no avail. I was pretty sure my surface was fried.
So I called up Microsoft Support and requested a call - (received it in less than 30 seconds) and the tech I worked with solved my issue.
Step by step of what she did.
She asked me to press the windows button to see if the surface vibrates. - Mine did not -
Then she asked me to plug it into the power cord and see if the light turned on - Light did turn on -
Then she said press and hold the volume up button and the power button for 30 seconds.
After that then I had to press and hold the power button for 10 seconds.
Once that was done, she had me press the power button once.
And it worked!!! -- I was pretty shocked, I had just about given up and was thinking I needed a replacement at this point...
Ok, but after that, once my pro was booted up she had me use the search charm and search for "troubleshooting" - just run through the program, it looks for problems with windows updater and things like that.
After that we did a restart on my surface, and then I went through the setting charm > change PC settings >update and recovery > windows update > and then check for updates.
I had a few updates to install - and then once that was done we turned off my surface and turned it back on again to make sure everything was working.
Hopefully this helps someone going through what I did. I was pretty sad last night when my surface wouldn't turn on.
Best of luck