I have a 1998 Grand Prix SE 3.8lt engine. The car has died with dimmed lights and weak cranking when trying to restart. A battery charger was applied and it started. It ran for a while, seemed ok. I tried to give it some gas, rev the engine and it started to bog with lights going dim and eventualy dying out. Will not start again. Poor cranking power. Battery or alternater, or both? Or something else?

Optional Information: 1998 Pontiac grand prix 3.8l