Battery Dead problems of the 2004 Acura RL

I tried starting my car and all of a sudden, my battery went dead. All the gadgets on my dash and not one could tell me my battery was dying or low on charge. So I call aaa and they replace the battery and all of a sudden my car is working better and my ac is working better. All the times I complained to the Acura dealership that my ac was not cooling properly in this florida heat and they check it and they tell me it's working just fine. All of a sudden, I get a new battery and my ac is working much better and now my car is really cooling down. No warning light came on telling me low battery. A car with all these electronics and no warning and the Acura dealership in delray beach checked it out numerous time and did not know that the ac was not functioning correctly because the car needed a new battery. Shame on Acura.