On March 28, 1999, at 1730 central standard time, a Piper PA-28-161, N82164, operated by Charterstar, Inc., was substantially damaged during landing rollout at Ankeny Regional Airport, Ankeny, Iowa. The airplane veered to the left side of the runway and hit a runway light after a landing from a touch and go. The airplane departed the runway and continued going down the embankment on the side of the runway. The airplane impacted a barbwire fence and went into a creek. The student pilot was not injured. The 14 CFR Part 91 flight had departed Ankeny Regional Airport on a local flight. Visual meteorological conditions prevailed and no flight plan had been filed. The student pilot reported that he landed slightly left of centerline but aligned with the runway. He reported the airplane began to swerve to the left and he applied an increasing amount of right rudder. He reported the airplane was going fast enough that it resisted the application of right rudder. He reported he determined the airplane had sufficient airspeed to lift-off so he applied full throttle and released the right rudder application. He reported the airplane departed the side of the runway, but he thought the airplane had enough airspeed to become safely airborne. He reported the airplane became airborne, but it was unable to climb and it settled back to the ground and came to a stop very quickly. The pilot reported that the engine was not sputtering or missing. An Operations Inspector from the Federal Aviation Administration reported that the ground where the airplane came to rest was about 40 feet lower than the runway. The inspector reported there were no skid marks on the runway that indicated the pilot had tried to stop on the runway.