During the initial climb after takeoff at about 300 feet, an unusual noise was heard by the pilot and the passenger who was recording the takeoff on a video camera recorder. The noise was a metallic tapping sound which varied with engine RPM. The pilot attempted to land on the remaining runway. The airplane overran the runway threshold and collided with a security fence. A post crash examination of the airplane and a test run of the engine failed to duplicate or explain the sounds as recorded on the tape. Further examination of the tape by an FAA approved engine repair station personnel concluded that the noise was a metallic 'tappet' type of a sound. During a disassembly of the engine a sticking exhaust valve was found in number two cylinder with evidence of high temperatures and oil burning residue on the springs of that valve. Textron Lycoming addresses the potential problem in Service Bulletin Number 388A, dated April 14, 1978, which recommends compliance at 1000 hours of operation. Lycoming Service Letter L197A, dated January 19, 1988, contains recommendations to avoid valve sticking. Lycoming Service Instructions 1425A, dated January 19, 1988, contains suggested maintenance procedures to reduce the possibility of valve sticking. No record of compliance was found.