2005 Aveo won't remain running

My wife's 2005 Aveo w/50,000 miles. Last nite the car barely wanted to start, and when it did start the headlights were very dim, I shut down the engine to tighten the bolts on the battery, then the car would not start at all. This morning I jump started the car with my car and the car started right up, but after disconnecting the cables the car would die. Does anyone know what might be the cause of this? Could it be that the alternator needs replacing?

I would be willing to say the alternator has craped out on you. get it tested at the auto parts store befor forking out all that money on a new one just to be sure.