Could be a number of things:
1. Faulty charger
2. Faulty internal psu
3. Even seen faulty power buttons in laptops before
Some very basic checks to rule out:
Try a different power socket in the wall
Replace the cable between the wall and the external power supply unit (if in two parts)
Replace the external power supply unit
If that doesn't do it I would be considering a RMA to ASUS
PacManCan