During the preflight inspection, the 305-hour private pilot visually inspected both fuel tanks and estimated that he would have enough fuel for two hours of flight with an additional twenty-minute fuel reserve. The pilot then departed and climbed to 5,500 feet to perform as an air traffic relay station in support of helicopters operating in the Gulf of Mexico. Upon completion of his mission, while the airplane was descending back to the originating airport, the engine lost power. The pilot elected to land in a marshy field and during the landing roll the airplane nosed over, coming to rest in an inverted position. No fuel was present when the airplane's wings were removed for recovery. The tachometer reading recorded by the pilot before takeoff was 770.9 hours and was noted as 773.2 hours at the accident site. The total elapsed time was two hours and twenty minutes.