I believe this may be an issue of a dirty heat sink and fan. I have seen this happen many many times, when I strip down the laptop to remove the heat sink and fan I often find a dust and lint clogging up the heatsink. It is almost like pulling out a piece of felt. Once this is removed the system will power up fine. You can sometimes use a can of air to blow out the dust, but on many systems that have a poor design you will not be able to remove the lint/dust without disassembling the laptop. The reason it shutsdown is to prevent the cpu from over heating, it will automatically shutdown the computer when the cpu reaches a certain temperature. It may also be a problem with the Nvidia chip. The only way to repair it would be to reflow the chip or replace the motherboard. The Nvidia chip may need to be reflowed. That means it has to be heated to a temperature that is high enough to melt the solder but not so hot as to burn up the chip.
