As normal, I left my Surface Pro plugged in overnight. And yes, the white LED is lit.
When I tried to awaken it:
The power supply WAS working. I plugged various things into the USB port on the brick and it is working. The LED tip is white as it should be.
I’d tried everything at http://www.microsoft.com/surface/en-us/support/warranty-service-and-recovery/surface-pro-wont-turn-on and things like http://www.winrtsource.com/2013/01/16/microsoft-surface-wont-power-on-solution/
For whatever reason, after reading everything on the web about reviving Surface Pro’s, I tried one more thing.
I Held the power button down and pressed the volume UP button. Eureka. Crisis averted. Normal startup. I did a cold shutdown, reinserted the microSD card which I had pulled for trouble shooting.
The battery is not depleted:
Now, if someone from the Surface team can tell me what exactly happened here…