A laptop can turn off for various reasons. Components could be broken or overheated; the circuits could be over- or under-powered or even short circuited. There are some protection mechanisms in place that immediately turn off the laptop when something out of the specifications is measured. You need to diagnose the circuits that supply power, consume them and produce heat.
First clear out the power to make sure the protection mechanisms are reset, as described in your question. Then, you measure the voltage and ampere of the power supply. In a sufficiently disassembled laptop it is also possible to further measure the power circuit near the power connector.
To diagnose whether or not it is the motherboard or something attached to it you need to start unplugging anything that is removable such that you get an idea as to whether that allows the system to boot further or not. Also check if there is too much heat in the cooling system near the CPU/GPU/Transistors/Caps/... in case your system has turned off at a non-POST time.
Finally, when you put them back ensure that the contacts are clean and all screws are back in place.