According to the student pilot, after finishing several takeoff and landings with his instructor, he was completing his first series of solo takeoff and landings. The first takeoff and landing was uneventful. During the second takeoff attempt, he stated that after applying full power on the takeoff roll, the airplane started shaking in the front and going to the left. He put in full right rudder, but the airplane continued going to the left. The pilot stated that he pulled the power back to idle and applied the brakes. The airplane exited the left side of the runway and went into a construction ditch, which resulted in substantial damage to the engine firewall and left wing. The pilot stated that he felt there may have been a mechanical problem with the nosewheel, rudder, or brakes. Examination of the wreckage by a Federal Aviation Administration inspector revealed no preexisting mechanical anomalies that would have precluded normal operation of the airplane.