The pilot reported that after he had taxied to the runup area, he decided to shut down the engine and verify the fuel levels. Afterwards, he attempted to restart the engine and found that the battery was dead. He exited the airplane, chocked the left main landing gear, set the throttle and magneto switch before he hand propped the engine. . . After the engine started, he removed the chock from the left main landing gear and attempted to re-enter the airplane. As the pilot re-entered the airplane, the throttle lock loosened, and the airplane accelerated forward without the pilot in the airplane. The unoccupied airplane subsequently impacted an airport fence, which resulted in substantial damage to the engine mount. The pilot reported that there were no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation.