The pilot reported that he conducted a walk-around of the airplane before boarding for the accident flight. After engine start, he noted more fuel in the right tank with the fuel totalizer reading 9.8 gallons and selected that tank for takeoff. After departure, while in the climb, the airplane experienced a total loss of engine power. The pilot stated he pitched the airplane forward and switched the fuel selector to both tanks just before they impacted trees at the end of the runway, which resulted in substantial damage to both wings. The pilot turned off the power and closed the fuel selector valve before egressing the airplane. During a post-accident examination, the fuel strainer was drained and a trace amount of residual fuel was present. Three of the 4 wing tanks were opened with fuel in both left tanks, but the right inboard tank showed no fuel and the right outboard tank was inaccessible. Additionally, the airport owner reported that he met the pilot on the runway after the accident, and the pilot stated, “the engine quit”, and “fuel may have been an issue.” The pilot reported no preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation.