The pilot reported that he utilized the asphalt portion of the 5,100-foot long runway due to the dirt portion of the runway being rough and containing loose rocks. During takeoff from the 1,300-foot long asphalt surface, which was the area closest to the departure end of the runway, the airplane rotated at the normal takeoff speed, however, did not climb as he expected. Subsequently, the airplane struck a fence, which resulted in substantial damage to the right wing and rudder and came to rest upright beyond the departure end of the runway. The pilot further reported that he felt the airplane did not climb due to the high density altitude and crosswind present at the time of the accident. Using reported weather conditions about five minutes prior to the accident and airport elevation of 3,075 feet mean sea level (msl), the National Transportation Safety Board investigator-in-charge calculated the density altitude to be about 6,389 feet.