You have already determined that your laptop charger is functional, but your computer still does not turn on. In addition, you have also tested that your laptop does not turn on when plugged in. If this is the case then the battery is most likely dead/drained and you must replace it.
Turn the computer upside down with the battery facing you.
Push the switch as far to the right as possible to unlock the battery.
Remove the battery using two hands and pull it away from the computer.