On June 7, 2001, about 1810 eastern daylight time, a Cessna 172M, N6863H, was substantially damaged during a precautionary landing at the Boire Field, Nashua, New Hampshire. The certificated flight instructor (CFI) and student pilot were not injured. Visual meteorological conditions prevailed and no flight plan was filed for the local instructional flight conducted under 14 CFR Part 91. According to the CFI, as the airplane was taxiing to the runway, he noticed a "skip" in the engine. When the CFI and the student performed a pre-take off run up, the left magneto was "rough." The CFI increased the engine power to 2,000 RPM and leaned the mixture until the "roughness" was gone. The airplane was then taxied to the runway for departure. During the takeoff climb from runway 32, a 5,501-foot long asphalt runway, approximately 100 to 200 feet AGL, the "skip" in the engine was experienced again. With about 1/3 of the runway remaining, the CFI elected to abort the take off, and descended the airplane at a steep angle towards the runway. The airplane impacted the runway with the nose wheel, bounced back into the air, and departed the end of the runway. The airplane touched down a second time on the nose wheel in a grass area, flipped over and came to rest inverted. A Federal Aviation Administration inspector examined the airplane after the accident and noted no discrepancies with the engine or ignition system.