The airline transport pilot reported that he configured the airplane with 10º of flaps during a soft field takeoff with a takeoff run of about 600 ft. After the initial climb, about 75 knots, he retracted the flaps, trimmed the aircraft for normal climb, and verified full engine power. About 100 ft above the ground and about two-thirds down the runway, the airplane started to decelerate to about 65 knots. He leveled the airplane and did not hear the stall warning horn activate nor recalled if the engine RPMs decreased or if the engine failed producing power. The airplane continued to decelerate and rapidly descended even when the pilot verified that the throttle was full open, the mixture full rich, the carburetor heat off, and the elevators at neutral position. Before impact, in an attempt to level the airplane, he smoothly pulled the yoke aft, but the airplane did not pitch up. The nosewheel impacted the ground and the airplane nosed over. The tailcone and both wings were substantially damaged. A post examination of the airplane by the Federal Aviation Administration inspector, engine and airframe continuity were confirmed. The inspector further reported that the s-bend damage to the propeller was consistent with the engine producing power. The inspector added that there were no mechanical failures or malfunctions with the airplane that would have precluded normal operation.