Is the battery removable at all? If it is, remove the battery, hold in the power button for a minute, plug in the battery and see if it works after that. If you can't remove the battery, unplug from wall power, hold in the button for a minute or a bit more, plug in the charger, hold in the power for about a minute see if it turns on OK after that on battery.
That laptop should be new enough to be in warranty, did you contact ASUS already?