My also broke his screen on his HTC EVO 3d. He sent the unit into HTC and was told that his screen broke because of a defect on the edge of the screen that wasn't seen because it was enclosed by the frame. They repaired it for free and all he paid was the shipping charge when he sent it to them, they paid return shipping charges.
I say all this because its hard to imagine a 4 year old being able to do this type of damage unless she had your toolbox in her lap and could grasp and use a ball peen hammer. Seriously though, hopefully you'll find that yours was also defective in some way. Good Luck with it.