When you power it on by holding the power button and then connecting the charger, you're essentially telling the system to ignore the sensors on the main logic board that prevent it from powering on if there is a problem and to power on anyway. The implication seems to be that there is a fault on the main logic board, possibly with the SMC or sensors. You'd probably need to do some board level diagnosis / testing to figure out the cause of the issue. Good luck!