It sounds like your laptop probably isn't getting any power from the charger. My grandchildren have two of these and as you might guess, they're pretty hard on them so they keep me busy trying to keep them running. There are three main reasons for no power conditions on these computers.
# Charger has died. Measure the voltage coming out of your charger; it should be running about 19 DC volts. If there's no power, pull the wall cord and verify that you've got 110V AC going in. I've had to replace or repair a couple of the cords going to the laptop on these guys; you can get an exact replacement on eBay. They're a bit of a pain to replace since the charger case is glued together, but it's doable. Otherwise you can just buy a replacement charger fairly cheap.
# The power connector on the motherboard is broken. I've had to replace a couple of these too. With enough abuse, the solder joints or the connector itself breaks and severs the connection between the charger and the motherboard. You have to open up the case, remove the motherboard and solder a new connector on; not a job for the casual do-it-yourselfer. If you're halfway competent at soldering it's not a terrible job though.
# The battery itself has died. This is actually an easy repair, but in your case I'd tend to rule this out since even with a dead battery the laptop should still come on when it's plugged into the wall socket.