On October 2, 2006, about 1605 central daylight time, a Piper PA-23-250, N71TA, piloted by a flight instructor and dual student, was substantially damaged during landing on runway 12 (5,010 feet by 100 feet, asphalt) at the Southwest Minnesota Regional Airport (MML), Marshall, Minnesota. The nose gear failed to extend properly prior to landing and attempts to use the emergency gear extension system were not successful. The instructional flight was being conducted under 14 CFR Part 91 without a flight plan. Visual meteorological conditions prevailed. The flight instructor and dual student were not injured. The flight departed Madison Municipal Airport (MDS), Madison, South Dakota, about 1430. The flight instructor reported to the Federal Aviation Administration that he was on an instructional flight with the owner of the airplane who was not rated to fly the aircraft. The instructor and the student were doing touch-and-goes at MDS. On the fourth landing, the retractable nose gear would not extend. The instructor wanted ground personnel to get a visual of the gear so he diverted to MML to conduct a fly-by. Ground personnel reported that the nose gear doors were fully open; however, the gear remained in the well and the nose gear tire appeared to be cocked. Several attempts to lower the gear using emergency extension procedures failed. The instructor reported using the CO2 bottle as a last resort, which also failed to lower the gear. He subsequently decided to land the airplane in the grass adjacent to runway 12 at MML with the main gear extended and the nose gear retracted. The forward fuselage was subsequently damaged during the emergency landing. Post accident investigation conducted by the FAA revealed that when the nose gear assembly was turned slightly left the axle bolt area would contact the door structure. There were visible nose wheel marks on the right gear door. Examination also revealed that the gear system worked satisfactorily using normal operations as well as the emergency hand pump. Maintenance records indicated that, five days prior to the accident, during the 100-hour inspection, the nose gear was removed, disassembled and reinstalled. The records also stated that the upper nose gear trunnion was repaired at that time. The records indicated that the gear was cycled five times following the repair. Maintenance personnel reported that wheel marks were observed on the right nose gear door at the time of the 100-hour inspection.