The student pilot reported that he had been performing touch-and-goes and had landed left of the runway centerline. When he advanced the throttle, the aircraft “immediately pulled hard left due to its left-turning tendency,” and exited the left side of the runway. The student pilot attempted to continue the takeoff in an effort to overfly a sign, however the airplane’s landing gear impacted the top of the sign. The airplane then settled back onto terrain next to the runway, and the nose gear collapsed. As a result, the airplane sustained substantial damage to the forward fuselage. At the time of the accident, the pilot was taking off on runway 17 with wind 060° at 4 knots. The student pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.