Sometimes a hardware reset helps with the deep sleeps some of the Acer Chromebooks can go in. Unplug the charger from the wall and the device, wait 30 seconds, plug it into the device first then plug the cord into the wall. Next you are going to press three buttons.
Press and hold the the esc key and the refresh key (looks like the arrow in a circle, usually the 4th key in on the top row).
press and release the power button while holding down the other two keys. Release all the keys. Try pressing the power again and check for lights.
To note: If you hold the 3 buttons, esc, refresh and power too long it can bring up a recovery screen, just turn it off and back on again.