According to the pilot, during a time-building, cross-country flight, the airplane had multiple mechanical malfunctions. On the fourth leg of the flight, he departed the airport and noticed that the airplane was low on fuel. He flew to a nearby airport, landed, and added 10 gallons of fuel. After fueling, the airplane would not start, and the pilot asked maintenance personnel to jump the airplane's battery. Then, during taxi to the runway, he noticed that the "radios and other electronics" were inoperative, but he continued to the runway. During the takeoff roll, he was startled by a loud noise in his headset, which he believed came from the airplane's communication radio. He attempted to assess the problem during the takeoff roll, and the airplane veered off the right side of the runway into the safety area. After regaining control, he taxied back to the approach end of the runway. He performed a flight control check and an engine power check and departed the airport. The pilot reported that he then landed at a nontowered airport "to check out the aircraft." He performed another flight control check and an engine run-up but did not exit the airplane "because of the starting issue." The pilot then departed for the destination airport. He reported that he landed the airplane and taxied to parking. He recalled that he performed a postflight check of the airplane, but "other than grass and grass stains [he] did not see any damage." Later that evening, the airplane's owner informed the pilot that the left wing was damaged. The airplane sustained substantial damage to the left-wing spar and aileron.