Hello,
I just found this step in certain discussion.
Maybe this will work on your laptop.
1. Remove power supply and battery.
2. Hold power button down for 30 seconds.
3. While still holding down power button, insert power supply then insert battery.
4. At this point, the blue light and the charging light both came on, and the computer started properly.
Here's the link to see more about how it solved.
source: http://ccm.net/forum/affich-31465-laptop-shut-off-will-not-turn-back-on
Have a blissful day!
I have an Asus G751 with windows 10. If i turn off or sleep my computer It completely dies for a seemingly random amount of time. The power button has no response. There are no lights, not even for the battery being plugged in. After a few hours the lights come back and the computer is perfectly fine, fully functional again. Due to the seeming randomness of it I belive the issue is being triggered by software and not hardware, but im truely at a loss.

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