Laptop won't turn on when I press the power button

Try a full power drain, but with the charger unplugged. Holding the button while it's plugged in doesn't do the same thing. Unplug the adapter, unplug every USB device, hold power for 30 seconds, then plug the charger back in and press power once. The light on the brick only tells you the wall side works. The barrel plug or the jack inside the laptop can still be the problem, so wiggle it gently while you press power and see if anything flickers. Also check it's really dead and not just the screen: tap Caps Lock and see if the key light reacts, and put your ear to the vents. If you get nothing at all after the drain, it's the board or the jack and a shop is the right call.