The student pilot reported that he lined the gyroplane up on the centerline of the runway for takeoff. As the takeoff roll was commenced, the student pilot stated he looked down to check the gyroplane's airspeed indicator and when he looked back up the gyroplane was 2 feet above the ground and drifting right. The gyroplane rolled right and came to rest on its right side. The gyroplane sustained substantial damage to the rotor mast and horizontal stabilizer. The flight instructor reported that as the rotor was coming up to speed, he noticed the student pilot was holding the cyclic aft and to the right. The flight instructor reported he tried to push the cyclic forward and left but was unable to overcome the student pilot's cyclic inputs. The gyroplane rolled right and came to rest on its right side. The student pilot reported there were no mechanical malfunctions or failures with the gyroplane that would have precluded normal operation.