Will not turn on

Hello. MacBook 2009 a1342. The magsafe power adapter light will come on when connected. It went from orange to green, but my mac will not turn on. The battery is fairly new ( 3 years ago) and has been in storage for most of that time. I know I need a new Mag port for the computer because it is damaged. But the light on the charger does come on. Could that be my only problem? Or could it be more than the mag port on the computer (not the charger).

Thanks

Katie