Dead battery and reduced engine power

What is your question?

My husband's 2008 Pontiac Grand Prix was previously having issues with a reduced engine power, we had taken it to a mechanic and had a sensor replaced and it fixed the issue for awhile but it's been acting up again and not sure what the issue is, as the engine light isn't on so we can't get any code readings. Car also keeps having to get jumped before being able to drive it, but because there's no check engine light on, not sure what the issue is there. The car will turn over but will not start.