On October 27, 2016, about 1130 central daylight time, a Piper PA 28-236 airplane, N4376V, impacted terrain during a forced landing following a loss of engine power on takeoff at the Lexington Municipal Airport (4K3), near Lexington, Missouri. The private pilot and his three passengers were uninjured. The airplane sustained substantial damage. The airplane was registered to Letzig Farms Inc. and was operated by the pilot under the provisions of 14 Code of Federal Regulations Part 91 as personal flight. Day visual meteorological conditions prevailed for the flight, which did not operate on a flight plan. The flight was originating from 4K3 at the time of the accident and was destined for the Camdenton Memorial-Lake Regional Airport, near Camdenton, Missouri. According to the pilot's accident report, the preflight inspection he conducted included sumping all three fuel sumps and the fuel tanks showed approximately 25 gallons of fuel per side. He started the airplane and taxied to a run-up area. During the run-up everything checked out "fine" including the carburetor heat. Every instrument was checked and worked properly. The fuel tank selector was on the fullest tank. The pilot taxied to the departure runway and turned on the strobes and fuel pump. He announced the flight's departure and verified the propeller and mixture controls were full forward as he added full power. Everything responded "fine." He glanced at the oil pressure gauge during the departure rolled and it was in the green. The airplane lifted off fine and it started to climb. The pilot stated, "All at once it was like the engine lost all power." There was no "pop or [crackle]" or roughness from the engine during the loss of engine power. He lowered the nose, veered slightly to the left, and headed for an open field where the nose landing gear collapsed and the engine mount sustained substantial damage during the forced landing. A Federal Aviation Administration inspector examined the wreckage. He verified that there was spark on all cylinder's sparkplugs. The inspector confirmed fuel was on onboard, the fuel selector on a detent, no debris was in filters, and no other apparent anomalies were found that would have caused a loss of engine power. At 1115, the recorded weather at the Midwest National Air Center Airport (GPH), near Mosby, Missouri, was: Wind 140 degrees at 3 knots; visibility 10 statute miles; sky condition clear; temperature 14 degrees C; dew point 10 degrees C; altimeter 30.28 inches of mercury. GPH's temperature and dew point were plotted on a carburetor icing probability chart. The plot shows a probability of serious icing at a cruise power settings at the temperature and dew point reported about the time of the accident.