The private pilot reported that the airplane's approach and touchdown on runway 27 (2,088 feet by 130 feet, turf) were uneventful. The airplane did not decelerate as he depressed the toe brake pedals, although he felt pressure through the pedals. He repositioned his feet and attempted to apply brake pressure again without any effect on braking performance. The pilot realized that the airplane was going to run off the end of the runway and decided to shutdown the engine and turn off the master electrical switch. He was "standing on the brakes as hard as possible" when the airplane impacted an airport perimeter fence, traveled through a ditch, and onto a nearby road. The airplane was subsequently struck by a vehicle traveling on the road. The airplane received substantial damage to both wings and the engine firewall. Examination of the turf runway after the accident failed to reveal any skid markings that could be associated with the airplane's ground track. Local law enforcement surveyed the accident site and determined that the airplane touched down with 1,072 feet of runway remaining. According to the airplane's operating handbook, at maximum gross weight the airplane required about 600 feet to stop on a paved, level, and dry runway. The operating handbook did not provide landing performance data for a turf runway. Local weather observations indicated that the surface wind was from the west-northwest at 9 knots. The airplane was equipped with a hand brake and dual toe brakes. The hand brake can also be used as a parking brake in conjunction with a locking ratchet system. Once the hand brake lever is engaged, the use of toe brakes becomes ineffective. With the hand brake fully disengaged, the left brake system functioned properly when its corresponding toe brakes (pilot and co-pilot positions) were depressed during a postaccident examination. The right brake assembly had impact damage that prevented a functional test. The pilot stated that he had used the parking brake earlier in the day, but he had alternatively used the toe brakes during the engine run-up before departing on the accident flight. He concluded that the parking brake must have "partially engaged" sometime during the flight.