1) Does the Light come on when the charger is plugged in. There should be a light that comes on when you plug the charger in (Not turned ON).
If that light is on, but the computer will not turn on first try A) Unplug charger B) remove the battery C) reconnect charger and then try turning it on. If AC Plugged in light on, but computer is not powering on - then take back to where you bought it an exchange it. Do NOT try to fix as you may void your warrentee.
2) if the plugged in to AC light does NOT come on then the problem is the AC charger, or the Laptop. How did you determine the Charger Is WORKING? Only way is to measure the Output voltage (with a meter), or try a known GOOD AC charger. If the AC light does not come on when a known good AC adaptor is used - take back to where you bought it for exchange. If it works then go back to store and see if they will give you a "Good" charger, or just return the whole laptop for exchange.
Note: AC Charger is really a AC power Adaptor also commonly refered to as a "Brick).