On September 14, 1998, at 2100 central daylight time, a Cessna 172, N733XG, was substantially damaged during takeoff. A student pilot on his first night solo flight reported the airplane experienced a loss of power after the airplane had lifted off the runway. The student pilot landed the airplane on the runway, and then the airplane veered off the runway. The airplane rolled into a ditch about 100 feet left of the runway and nosed over. The student pilot was not injured. The 14 CFR Part 91 flight was departing the Harrisburg-Raliegh Airport on a local flight. Visual meteorological conditions prevailed and no flight plan had been filed. The student pilot reported the engine quit when the airplane had climbed to 5 to 6 feet agl. When the airplane touched down it veered left off the runway. The airplane went into a ditch where it nosed over. An Airworthiness Inspector from the Federal Aviation Administration examined the airplane. The engine exhibited continuity. No anomalies were found in the fuel and ignition system. The inspector reported there was no apparent reason for the power failure.