On my Asus N550JV laptop, if I push the power button, it lights up for half a second then turns off. The green indicator light on the front lights up when AC is plugged in.
I tried unplugging, removing the battery and holding the power button for 30 seconds, but this made no difference.
What should I diagnose?
There's a couple things to check as you surmised; the power cord/powerbrick, the adapter jack, and power button. If all those things check out, it is likely a motherboard problem.
The easiest way to test the power cord/brick and the adapter jack is to use the power brick on another laptop that has the same connector type, and see if it works or not. A multi-meter works too if you have one.
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.
Most likely the power supply unit is dead and needs replacement.
A professional can measure the electric current on entry and exit of the PSU. But the simplest test is to try another PSU. If you know how to open the laptop (I suppose it's no longer under warranty), you could even use a desktop PSU as long as as it has at least as much capacity - the PSU doesn't have to go into the case, only the wires do (this won't work if the PSU is soldered to the motherboard).
Otherwise, get help from a knowledgeable friend or a professional repairman.
Beyond testing power supply and battery, there is not much you can do at home.
Try starting it without the battery and any peripherals you can disconnect, if it still doesn't start best case scenario is power supply failure and you can use a cheap multimeter to measure its power output. If you are not sure how to use it DO NOT TRY TO, as you can get yourself killed (not likely but still). You can always ask around your neighborhood, someone is probably familiar with how to do this as a lot of people study electrical sciences.
Another very possible option is you motherboard is fried so there is not much you can do about it yourself.
It turns out that some internal parts such as memory were disconnected from each other.
Reconnecting them solved the problem.
Just had the same problem. Found that the ribbon cable from power switch to motherboard was not seated properly.
