The pilot reported that after flying for approximately 1.7 hours his engine started to run rough. He contacted the nearest control tower and reported the problem while trying to turn back to an airport he had just passed moments ago. After making a 180 degree turn the airplane's engine died and the pilot, who was unsure he could make it back to the airport without unduly endangering people on the ground, opted to set the aircraft down in an empty field. The landing was uneventful however on the landing roll the aircraft encountered a divot in the ground and nosed over on its back. After the aircraft was righted the FAA inspector on scene noticed the fuel filler cap on the right wing was missing and there were several blue stain streaks aft of the filler port to the trailing edge of the wing. After further investigation by the FAA inspector the fuel filler cap was found in the run up area where the pilot had last refilled his tank. Further examination of the fuel system found it to be intact with just 3 tablespoons of fuel in the fuel sump and no fuel in the main fuel lines to the injector when the boost pump was turned on.