Keeps shutting off?

Hi, I just sent you a question last week actually, thank you for answering. That it was very helpful. So, I have since then replaced my alternator, bought a new alternator yesterday and had it put in the car. As soon as it was put in the car, the car still would not start. Took the battery charged, it started but immediately shut off. Got the car jumped off shut off again. Took the battery had it charged completely was able to drive it almost home and it shut off again and would not start without being jumped off but would immediately shut off again. Okay, so, we took the battery he had it completely charged again was able to drive the car home. I thought everything was fine. The auto parts place check the battery, they said oh, it has a dead cell but the battery is okay. I don't know what that means or anything. All I know is that my car is now stranded on the side of the road actually right now because it won't start and honestly is not think it's going to do any good to get it jumped off again. So, do I need to take the alternator back off and see if it's a bad alternator or do I just need to buy a new battery or is it something else all together? Please help, I just don't know what to do. Thank you