Welcome to Android Central! First, try pressing and holding Power for 15-20 seconds. If nothing happens, plug it into a wall outlet and let it charge for at least 4-6 hrs undisturbed, then try powering on again. If that doesn't help, then try charging again with a different cable and wall charger plug.
If all of that doesn't work, then it could be a dead battery, a faulty Power switch, or a dead motherboard. In any of those situations, you probably need to bring it to a repair shop.