I would suggest give laptop a quick discharge first as following:
1. remove all power sources including the power adapter and battery
2. pressing the power button over 20 seconds do not let go
3. Then connect only power adapter charger, power on the laptop again.
Also, try remove the RAMs and power on as well, hear if there is any beep sounds.
Most shut off may cause by the overheated CPU, check the heatsink, reseat CPU and replace the thermal paste are good try as well. Check the CPU fan speed.
Hope this helps.