The pilot reported during preflight refueling he closed a fuel shutoff valve located at each wing root to prevent cross feeding. Upon starting the engine and preparing for takeoff the pilot verified that the main fuel valve was in the on position, but failed to open the fuel shutoff valve located on each wing causing the engine to run only from the approximate 1.5 gallons of fuel contained in the header tank. Just after takeoff the engine lost power as a result of fuel starvation. During the subsequent off airport forced landing the airplane sustained substantial damage to left and right wings, empennage, and vertical stabilizer. The pilot reported no preimpact mechanical failures or malfunctions with the airplane that would have precluded normal operation.