On May 24, 1998, about 1720 eastern daylight time, a Piper PA-28, N15913, was substantially damaged when it collided with terrain during the initial takeoff from Nellis Airport, Minden, New York. The certificated flight instructor received serious injuries and the student pilot received minor injuries. Visual meteorological conditions prevailed and no flight plan was filed for the instructional flight conducted under 14 CFR Part 91. The flight instructor reported that this was his first flight to the private airport, owned by the student pilot. He described the runway as being 2,700 feet long, not very wide, and with a slight curve. One end of the runway was aligned at 320 degrees, and the opposite end was aligned at 130 degrees magnetic. Both ends of the runway had culverts. The southeast end dipped, and the northwest end was humped. Before takeoff, the flight instructor and the student pilot walked the runway to observe obstructions and peculiarities. The flight instructor voiced his concern about the hump, and with light winds decided to takeoff to the northwest. In a written statement, the flight instructor said he was demonstrating a soft field takeoff. He stated that when the airplane hit the dip about 100 feet down the runway, it was as if it "catapulted them into the air in an extremely nose high attitude." The flight instructor reported that when the airplane did not respond to his control inputs he thought the student pilot was frozen on the controls, so he yelled, "I've got the airplane." He said he tried to keep the airplane flying in "ground effect" and attempted to turn the airplane to the right, towards the runway. The flight instructor stated the airplane traveled through grass which was 3-4 feet tall and impacted the ground. The student pilot stated that the instructor pulled the nose of the airplane up. The airplane then started to shake and the instructor commented on being "behind the power curve." The student pilot said the instructor then lowered the nose and "lost directional control of the aircraft." A Federal Aviation Administration Inspector stated that the airplane came to rest about 471 feet left of the runway after traveling through 24 inch tall grass and striking trees. He stated that the last 4 feet of the left wing outboard of the stall vane, including the entire left aileron, was laying on the ground. The Inspector reported that the engine mount was bent downward and the fuselage skin, from the engine area to about 6 inches beyond the firewall, was buckled. The flight instructor stated that he did not retard the throttle during the takeoff, and did not experience any mechanical problems with the airplane.