well, try the charger in a different outlet, maybe the outlet went bad. and there are several reasons why it wont turn on. it could be a dead battery, a component may have died, it could be an unplugged cable from the power button to the mobo, etc.
Does a light come on the front of the laptop when it is plugged in? As far as I have seen, you can remove the battery from most asus laptops by taking off the bottom pannel and then poping it out. Do they make asus laptops that you can not remove the battery from?
I just had the same issue with my Asus g752. I unplugged the charger, pressed and held the power button for a good minute or so, until the thing just sprang to life again, then died. I plugged it back in and hit the power button again, and it turned back on again, and everything worked great. Hope this helps.