If it cannot be powered on while connected to the charger and the battery is inserted, it seems to indicate that your battery is faulty.
My battery is dead and it doesn't matter whether I plug it in or not. It will always power on telling me "charging, please wait" or "critical battery, please charge". If I press and hold the minus button and the power button to do a reset, it will initially tell me that there is 40% charge, but then immediately switch to critical battery. Without the battery, the sound sometimes is noisy and distorted, supposedly from lack of power.