The pilot reported that the aircraft's park brake was unserviceable but the foot brakes were serviceable on departure from Greenhills. Whilst taxiing to the parking area, after landing at Jandakot, the brakes failed completely. In an attempt to avoid a ditch and parked aircraft, the pilot started a 180 degree turn using the rudders. After approximately 90 degrees, the aircraft collided with a parked Cessna 310. At no stage prior to the collision did the pilot attempt to stop the aircraft by shutting the engine down.