On April 14, 2000, at 1547 hours Pacific daylight time, a Piper PA-28-161, N81019, was substantially damaged during an off airport landing following loss of engine power during takeoff initial climb. The commercial certificated pilot was not injured. Visual meteorological conditions prevailed for the local area, post maintenance check flight operated by the Palo Alto Flying Club under 14 CFR Part 91. No flight plan was filed. According to the operator, the aircraft had just received an engine oil change and it was the operator's practice, following maintenance, to fly the aircraft around the airport traffic pattern a couple of times before releasing it for student use. The pilot/flight instructor told the operator that the start, taxi, and run-up were normal. The engine operated smoothly until, at 300 feet agl on takeoff climb out, the engine quit abruptly, regained power, then quit again. The pilot attempted to return to the departure runway but landed short in a marsh area. The operator further stated that, at the accident site, the propeller did not appear to have been turning on impact. There was fuel in both wing tanks and there was no contamination at the sumps. The emergency responders had instructed the pilot to turn the fuel selector to the "off" position. The fuel pump functioned audibly. There was clean oil in the engine and the engine rotated freely with good compression. After recovery, the cowling was removed and the engine was examined by inspectors from the Federal Aviation Administration San Jose Flight Standards District Office. No anomalies were noted. The propeller was replaced and the carburetor heat box was removed due to damage. The engine started promptly, the run-up was normal, and the engine delivered full power. It was noted that, if the fuel tank selector valve was moved out of a tank position detent to the between-tank or off position, the engine operated approximately 1 minute before stopping.