The student pilot stated that he was practicing a soft field takeoff and as soon as the nose wheel lifted off from the runway, the airplane veered to the left. The student pilot tried to correct the turn by applying right rudder and aileron, but was unsuccessful. The airplane departed the runway surface and came to rest nose down on a parallel taxiway. The airplane sustained substantial damage to the engine nose wheel area, both wings, and the fuselage. The student pilot did not report any preimpact mechanical malfunctions or failures with the airplane.