On June 16, 2018, about 1315 eastern daylight time, a Piper PA-28-140 airplane, N1782J, was substantially damaged when it was involved in an accident near East Hartford, Connecticut. The pilot and passenger were not injured. The airplane was operated as a Title 14 Code of Federal Regulations Part 91 personal flight. The flight departed Hartford-Brainard Airport (HFD), Hartford, Connecticut. The pilot stated that after takeoff, when the airplane was about 900 ft above ground level, the engine started to sputter and lost partial power, and the airplane would not maintain altitude. He decided to conduct a forced landing on a runway at a nearby closed airport. During the descent, the pilot verified the mixture was full rich and the carburetor heat was off, and he switched fuel tanks. The pilot said the engine did not respond, so he turned it off and executed a "forward slip" and S-turns to position the airplane onto the runway; however, the airplane landed about 600 ft from the departure end of the runway, overran the end of the runway, and struck a fence. The pilot reported he believed that the recently replaced fuel selector valve failed and starved the engine of fuel. The airplane sustained substantial damage to both wings and the fuselage. An on-site examination revealed that the airplane was not leaking fuel, and fuel was present in each wing tank. The fuel drained from the tanks had no evidence of contamination. An engine test run revealed that the engine ran with no defects noted in the following scenarios: on the right fuel selector position to full power, on the left fuel selector position to full power, in both fuel selector positions to full power with the fuel boost pump turned off, with both magnetos selected, and with left and right magnetos individually selected. No hesitation or loss of power was observed. Fuel that was recovered from the airplane’s wing fuel tanks was used for the engine test run. At 16:53, the recorded weather conditions at HFD were as follows: wind from 010° at 8 knots, visibility 10 statute miles, clear, temperature 28°C, dew point 9°C, and altimeter 29.97 inches of mercury. Weather conditions about the time of the accident were plotted using the chart in Federal Aviation Administration Special Airworthiness Information Bulletin CE-09-35 regarding carburetor ice prevention; the weather conditions (ambient temperature of 28°C and dew point of 9°C) were conducive to serious carburetor icing at glide power.