Powering On - If a Chromebook (CB) is charged, opening the lid will usually power on the CB. Sometimes you may have to push the power button (upper right) for a second or two before the CB comes on.
Sometimes the CB goes into a sleep mode. Try this:
Shut CB Lid.
Plug in Power Cable
Open CB Lid wait about 4 seconds
If nothing happens, hold the power button for 3 seconds.
If still nothing happens. Pull power cord, plug power cord back in and repeat the process. Try opening and closing the lid a few times and then push the power button.
A video that helps you troubleshoot a Chromebook that will not come on