The instructor was demonstrating a powered approach to his student but this required the student to take control once on the ground, including application of the brakes. After touchdown, the student applied the brakes but felt that the aircraft was not slowing down. The instructor tried to shut down the engine using the magneto switches but because of a broken grounding wire, it continued to run. The student tried to steer the aircraft to avoid the boundary fence, but it was travelling too fast and rolled onto its right side. Neither occupant was injured.