Main computer battery does not charge.
Battery is bad.
Battery charger board is bad. It is possible that if the power plug is good that the computer battery is bad. Leave the computer connected to the power with the battery connected in the computer for at least one hour, if the battery does not charge consider having the battery and or the laptop serviced or repaired. If the computer and or battery is not in warranty consider just replacing the battery as it is very likely that it is just a bad battery. If the battery has been replaced or an alternate battery from an alternate identical laptop does not work in the computer it is likely that the power or charger board within the laptop is bad.