What happens to energy when a car runs into a wall?

The energy is partially transferred to the wall and partially to the car. However saying that this is why the car gets damaged is a bad way to formulate it: the car gets damaged by the forces acting on it. Energy, while characterizing this process, is not identical with the process itself, and is not itself performing any action. Energy calculation is certainly a good way to estimate the amount of damage, e.g., by expressing it in kilograms of TNT.