Drained/dead Battery
The first thing to check for when your Chromebook won't turn on is a dead battery. Plug the unit in via AC charger and let it charge for at least 30 min to an hour and try turning it on again.
Blank Screen
A "blank screen" is when the light on the power button is on, but the screen remains black.
First try powering your Chromebook off by holding the power button down for six seconds, then turning it back on again.
If powering off does not work, then press "Refresh" and "Power" buttons for 10 seconds until the computer returns.
This may take at least 15 times.
Overheated computer
If no lights turn on when the power button is pressed and the computer is very hot on the bottom, your computer may be overheated. You will have to wait a few minutes until it has cooled down. Unplug the laptop from its power cable and let it sit with the vents unobstructed. After at least 10-15 minutes, try turning the computer on again. If it boots normally, the computer was too hot. Try using the Chromebook on a hard surface to help prevent this in the future.