My Acer Notebook was warning low battery. I did not plug in soon enough and it shut off. I have now plugged it in to the charger, but will not turn on. When I press start button the battery light flashes briefly then shuts off. I have never not had it turn on with the charger attached. It is fairly new by the way, just 3 months.
Unfortunately, I have seen this all too often. This means that the AC soldering on your motherboard either burnt out or broke. That means that when you put the AC cable into the socket, the power is not able to be connected and is not able to charge the battery.
Hopefully it is still under warranty because the best option is to have the motherboard replaced. You could have the soldering re-soldered but there no guarantee that it won't short/burn out the motherboard.
They certainly don't make them like they used to. I see this all the time and I even had it happen to my own laptop. Unfortunately for me, I dropped $500 into it before declaring it dead and scavenging it's innards.
Anyways, good luck!
P.S. If you end up getting a new laptop, stay away from Acer, Dell, HP and others like that, they are REALLY cheaply made! How do you think Michael Dell became a billionaire?