The pilot reported that, during a short-field takeoff, around 100 ft above the ground, he saw the primary flight display (PFD) airspeed indicator showing 0. He added that the engine appeared to be functioning normally, but he decided to level the airplane and attempt to land on the remaining runway. The airplane then began to turn left, and he added right rudder. Subsequently, the airplane touched down on an adjacent taxiway left of the runway, and the nose landing gear collapsed. The airplane sustained substantial damage to the left horizontal stabilizer. Postaccident examination videos were provided by a Federal Aviation Administration inspector. The videos showed both the PFD and backup airspeed indicators moving in sync with air applied to the pitot tube. The automated weather observation system at the airport reported that, about the time of the accident, the wind was from 190° at 10 knots, gusting to 18 knots, and the calculated density altitude was 7,883 ft. The pilot was departing from runway 24.