On November 28, 2000, about 1200 Eastern Standard Time, a Piper PA-28, N5035W, was substantially damaged after a partial loss of engine power and an aborted takeoff from Lebanon-Warren County Airport (I68,) Lebanon, Ohio. The certificated flight instructor and commercial pilot received minor injuries. Visual meteorological conditions prevailed for the personal local flight that was conducted under 14 CFR Part 91. According to the pilot, this was the first flight since the airplane had undergone maintenance for engine mount and propeller repairs. The airplane was removed from the hangar and the pilot conducted a preflight, to include draining the sumps and carburetor. The pilot added that since the airplane had just come out of maintenance, he looked at it more closely than normal, especially the engine compartment. Once satisfied with the airworthiness of the airplane, the pilot boarded and taxied to pickup the instructor who just wanted to go for a ride. With the instructor onboard, the pilot taxied the airplane short of Runway 18, a 4,502-foot long runway, and preformed the engine run-up checks. He checked the magnetos, and carburetor heat. In both cases, he identified no anomalies. With the run-up checks completed and 10 degrees of flaps, the pilot taxied onto the runway, advanced the throttle, and departed. Once airborne, the pilot climbed the airplane to 4,000 feet msl, and the pilot and instructor conducted some upper air-work. Satisfied with the airplane's performance, the pilot descended and maneuvered the airplane onto a left downwind leg for a touch-and-go on Runway 18. The pilot completed the base leg portion of the traffic pattern and then turned final. Once on final, the pilot selected 10 degrees of flaps, and the airplane touched down in the first 1/4 of the runway. The pilot advanced the throttle for takeoff, and the airplane accelerated. The takeoff sequence was normal until the airplane reached approximately 10 to 15 feet agl, and the engine loss partial power. The pilot aborted the takeoff, and the airplane touched-down on the runway with 1/3 remaining. As the airplane touched-down, the instructor stated he had the controls. The pilot released control of the airplane, and the airplane departed the right side of the runway, hit a berm, and came to a stop 1,400 feet short of the departure end. According to the flight instructor, the pilot added power to execute the takeoff portion of the touch-and-go. The engine responded, but when the airplane was approximately 150 feet agl, the engine started to run rough. The instructor told the pilot to switch the electric-fuel-boost pump "ON," but was not sure if the pilot actually got the switch to the "ON" position. The instructor applied right rudder to direct the airplane to a sod farm that boarded the runway. When he did, the pilot asked "where we going?" The instructor responded "sod." The airplane touched down on the sod, and then contact a 3-foot high berm before coming to a stop. When the flight instructor was asked why he directed the pilot to land on the sod, and not the runway, he stated that he was concerned they would not get the airplane on the ground and stopped before reaching some buildings at the far end of the runway. According to a Federal Aviation Administration inspector, on December 18, 2000, an engine run was conducted. Before the engine run, the fuel sumps were drained and found absent of debris. Some mud was removed from the air intake, and the engine was preheated. When the starter switch was engaged, the propeller rotated three times and then the engine started. The engine ran rough for approximately 3 seconds then smoothed out. The engine run lasted approximately 2 minutes, and because of propeller damage, was limited to 600 rpm.