The pilot reported that, during takeoff following a touch-and-go landing, the engine gauge readings appeared normal, the airplane lifted off the ground about 65 knots, and he applied nose down pressure to stay in ground effect. The pilot reported that the airplane was not showing indications of a climb nor was the airspeed increasing, so he lowered the nose further. He then attempted to climb by pulling back on the yoke and alternately build airspeed by lowering the nose multiple times with negative results. The pilot then reduced power to abort the takeoff. The airplane landed on the remaining runway, overran the end of the runway, and impacted a fence. The airplane sustained substantial damage to the fuselage and both wings. The pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation. The passenger in the right seat provided a video showing the touch-and-go landing from the right seat looking forward through the windscreen. The instrument panel cannot be seen. During the landing, the airplane touched down about 200 feet beyond the approach end of the 3,004 ft. long runway. The pilot applied takeoff power, the airplane lifted off the runway, and continued in level flight in ground effect. The pitch attitude did not appear excessive, the stall warning horn was not audible, and there were no abnormal sounds from the engine. The pilot then reduced power to abort the takeoff. The airplane touched down near the departure end of the runway, and the camera panned downward for the remainder of the video.