On September 19, 2016, about 1700 mountain daylight time, a Piper PA 32R-300 airplane, N4477F, impacted a tree and terrain during a forced landing near Grants, New Mexico. A ground fire subsequently occurred. The pilot and two passengers were uninjured. The airplane was destroyed during the impact and ground fire. The airplane was registered to and operated by the pilot under the provisions of 14 Code of Federal Regulations Part 91 as a personal flight. Day visual meteorological conditions prevailed for the flight, which did not operate on a flight plan. The flight was originating from the Grants-Milan Municipal Airport (GNT), near Grants, New Mexico, at the time of the accident and was destined for the Cedar City Regional Airport, near Cedar City, Utah.According to the pilot's accident report, the pilot performed a pre-flight inspection. He taxied to the run-up area for runway 31 and conducted the before takeoff checklist. He taxied the airplane to the beginning of the runway and set the throttle to full power. The roll-out and acceleration was considered to be normal. The airplane lifted off approximately 5,000 feet down the runway at 80 knots. Approximately 100 feet above ground level and about two 2 seconds after lift-off, he heard a "gurgle" and the airplane lost engine power. The pilot verified that the fuel pump was on and the throttle was in its full position. He turned the airplane about 20 degrees to the left and determined the airplane would not be able to return to the airport at its altitude at the time. The pilot located a landing site and he landed the airplane in between two trees. During the landing roll, the airplane turned to the left and headed for a tree. He was unable to correct the heading with applied right rudder. The airplane impacted a tree and the airplane caught on fire. The pilot and passengers exited airplane and ran away from fire. N4477F was a 1976 model Piper PA-32R-301 airplane with serial number 32R-7680449. The airplane was a low-wing, all-metal, single-engine, six-place monoplane. It had a retractable tricycle landing gear configuration, and was powered by a fuel injected, six-cylinder, Lycoming IO-540 engine with serial number L-15137-48A, which drove a Hartzell variable-pitch propeller. At 1655, the recorded weather at GNT was: Wind calm; visibility 10 statute miles; sky condition clear; temperature 30 degrees C; dew point -13; altimeter 30.28 inches of mercury. The local temperature and dew point were not in the range conducive to carburetor icing. GNT was a public, non-towered airport, which was owned by the City of Grants, New Mexico. It was located about three miles northwest of Grants, New Mexico. The airport had a surveyed elevation of 6,536.9 feet above mean sea level. The airport's runway 13/31 was 7,172 feet by 40 feet with an asphalt surface. A Federal Aviation Administration Air Safety Inspector examined the wreckage. The Inspector, in part, indicated that the airplane was badly damaged by fire. However, the fuel selector handle was not in the "full on" position for selecting a fuel tank. An image of the fuel selector valve showed it was found selecting a position by the left tank position and the off position. The Piper service manual, in part, stated: 8-18. FUEL SELECTOR VALVE OPERATION. When the fuel selector handle is not in a positive selector detent position, more than one fuel port will be open at the same time. It should be ascertained that the fuel selector is positioned in a detent, which can be easily felt when moving the handle through its various positions. Piper Service Bulletin (SB) 772, in part, stated: PURPOSE: It has been determined that certain Cameron l-H65-3 Fuel Selector Valves (Piper Part Number 69735-0SV) may exhibit excessive freeplay between the valve shaft and arm. If this condition exists and is left uncorrected, the indicated selector valve position may not correspond with the actual position of the selector valve, resulting in partial or restricted fuel flow through the valve ports, and possible loss of power. ... INSTRUCTIONS: During Each Preflight: 1. Move the Fuel Selector Control into each of its three positions -Off, Left, and Right - to insure that a positive detent is present at each of the three positions. 2. If positive detent is not exhibited at any of the three positions, the Fuel Selector Valve must be replaced before further flight. The installed version of the fuel selector valve could not be determined due to the fire damage it sustained. The Pilot's Operating Handbook (POH) current at the time of the accident, in part, stated: ENGINE POWER LOSS DURING TAKEOFF If sufficient runway remains for a normal landing, leave gear down and land straight ahead. If area ahead is rough, or if it is necessary to clear obstructions: Gear selector switch..................................................UP Emergency gear lever (on aircraft equipped with backup gear extender).locked in OVERRIDE ENGAGED position If sufficient altitude has been gained to attempt a restart: Maintain safe airspeed. Fuel selector.................. switch to tank containing fuel Electric fuel pump....................................................ON Mixture................................................................. RICH Alternate air........................................................ OPEN Emergency gear lever.................................. as required If power is not regained, proceed with power off landing. The POH did not amplify or caution the pilot of the importance of ensuring the fuel selector is in a positive detent on a fuel tank selection position to the extent that the maintenance manual and SB explained it.