Getting to the moon imposes an energy cost that is far beyond the ability of the space shuttle to meet. In order to reach the moon, a spacecraft must accelerate to 6.68 kilometers per second. Reaching this speed requires a ship built within the rocket mass fraction.
The rocket mass fraction is set by the energy potential of the rocket fuel and the speed that must be achieved, which in the case of the moon is 6,680 m/s. The weight of the necessary fuel is then determined by the rocket equation. Unfortunately, the space shuttle was not designed within the rocket mass fraction required to make 6 km/s, and so even an infinite amount of fuel would not have enough energy to lift both itself and the shuttle to the moon.