The small mechanical key only unlocks the driver's door, and it does not start the car.
The key fob's battery allows it to communicate with the car's SS/SE, as well as to remotely lock or unlock the car.
If the fob's battery dies, then the fob cannot communicate with the car's SS/SE. That's why you have a small mechanical key, to unlock the driver's door. The fob can still be placed into the dashboard recepticle to start the car, even if the fob's battery is dead.