According to the pilot, he was conducting multiple "Young Eagle" flights of 10 to 15 minutes' duration each. After taking off on the fifth flight, and as the airplane reached 300 feet, the engine lost power. The pilot switched fuel tanks and verified that the fuel pump was on, but to no avail. He then force-landed the airplane on the departure end of the runway. However, the airplane continued off the end of the runway and through a grassy overrun for about 100 yards, until it impacted a fence, substantially damaging both wings. The pilot noted that there were two main fuel tanks and two auxiliary fuel tanks on the airplane, and that during the first four flights, he only utilized fuel from the left main tank. Prior to the fifth flight, both auxiliary tanks and the right main tank were full, and the left main tank indicated 1/4 full. The pilot initially switched fuel feed to the right main tank, but then decided to utilize the remaining fuel in the left main tank, and switched back to that tank before takeoff. Postflight examination of the left fuel tank revealed no fuel in the tank. The pilot also stated that there were no preexisting mechanical anomalies with the airplane.