The pilot initiated the takeoff roll from runway 30 with the throttle and mixture control in the full forward position. When the airspeed reached 65 knots, the airplane began to climb and the pilot noticed that the airplane was not accelerating. He flew over the departure end of runway 30 at 100 feet and started a shallow left turn. He noticed that the landing gear indicator lights were illuminated green so he adjusted the landing gear lever down and then up again. The pilot continued to be distracted when the green lights remained illuminated. He then decided to fly to runway 6 and make a forced landing. The airplane was still 100 above the ground and began to lose altitude. The pilot made a forced landing straight ahead into a field and the airplane struck several trees. Prior to departure, the fuel tanks were filled with 40 gallons of fuel and the airplane contained 40 pounds of luggage. The calculated density altitude for the flight was about 7,800 feet. The pilot reported that there were no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation. Based on the information gathered, it is likely that the airplane's performance was degraded due to a high density altitude and a rich fuel-air mixture.