On August 06, 2016, about 1145 eastern daylight time, a Piper PA-28R-201, N3783M, was substantially damaged during a forced landing following a partial loss of engine power near Northampton Airport (7B2), Northampton, Massachusetts. The flight instructor and pilot receiving instruction were not injured. The instructional flight was conducted under the provisions of 14 Code of Federal Regulations Part 91. Visual meteorological conditions prevailed, and no flight plan was filed for the flight, which originated from 7B2, about 1143.According to the flight instructor, during a simulated soft field take-off, the airplane's climb performance deteriorated noticeably. As the airplane reached approximately 150 feet above ground level, the engine started to lose power. He then realized that continuing the climb was not possible, and any increase in pitch resulted in an immediate decrease in airspeed. The flight instructor elected to make an emergency off airport landing in a corn field near the end of the departure runway. During the landing sequence the right wing and firewall were damaged. A post accident examination of the airplane by a Federal Aviation Administration inspector revealed that the alternate air valve plate had separated from its mounting location and was lodged in the fuel servo air intake, blocking the fuel servo. After further examination of the alternate air valve plate it was noted that the hinge pin was worn completely through the plate assembly. A review of manufacturer engineering drawings showed that the plate assembly was modified using a spring attached to the plate. A review of the logbooks did not reveal an entry of a modification, or repair of the part.