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Seems like overheating. When the processor is too hot (which happens a lot in laptops) the computer shut down by itself to prevent the cpu to be hurt. That's why you can't start it right after i guess. Try to get the dust out of the computer and try it again.
Sometimes, faulty capacitors or some problem in motherboard circuitry can also cause the computer to overheat. Get it checked from a computer repairshop. If your computer shuts down by itself, then it is possible that anyone of the above reasons, may be the cause of it.