Is my battery dead or could it be alternator or something else? Help!?

I try and start my car and it starts up for about 3 to 5 seconds then dies every time. I tried to get a jump from a buddy and it still didn't do anything. The lights in my car when the door is open still goes on so I'm not sure if it is the battery, unless the indoor lights use something else to power them. Also on my dash the battery light does turn on after I try and run the car and it dies. My car is a 2000 Pontiac GTP and this has never happened before. Could it be the battery or possibly the alternator? or something totally else?