What do you mean the trigger won't cock? The trigger does not cock, it does what we call reset after it is pulled and the hammer falls. resetting is the forward movement of the trigger when it is released.
if the safety is on the hammer cannot be moved, either to fire the gun or to cock if it is down. If the hammer is cocked and the safety on the slide can move. If hammer down and safety on the slide cannot move.
As christak said, it is single action only, meaning the hammer must be manually cocked before firing. This can be done by pulling the slide back, with the safety off, as chambering a round. When the gun is fired the reward movement of the slide recocks the hammer.