If I understand what you have said, you have the key fob that came with the car, and another one that you bought.
Does the key fob that came with the car start the engine without problems? If not, what happens when you try to start the engine with your original key fob that started your car some time ago?

I believe the key fob you bought recently cannot be expected to start the engine, so set it aside, and let's talk about the things that happen when you try to start your car with the old (original) key fob. If you do this, we will have a less confusing discussion, and (hopefully) a clear idea of what corrective steps to take.