On June 4, 2000, approximately 1130 Pacific daylight time, a Piper PA-20, N7737K, experienced a gear collapse during a forced landing about five miles west of Lake Quinault, Washington. The private pilot and his passenger were not injured, but the aircraft, which was owned and operated by the pilot, sustained substantial damage. The 14 CFR Part 91 personal pleasure flight, which departed Port Angeles, Washington, about two hours earlier, was being operated in visual meteorological conditions. No flight plan had been filed, and the ELT, which was activated by the accident sequence, was turned off at the scene. According to the pilot, about two hours into the flight, while cruising approximately 2,000 feet above ground level (AGL), he decided to switch from his almost-empty right wing fuel tank to his left wing fuel tank, which was full. At that time, he thought the right tank should have had about three or four gallons in it. Less than a minute after he moved the fuel selector, the engine quit. He therefore switched back to the right tank, but the engine did not restart. He tried both the left tank and the right tank one more time each, but could not get the engine to restart. Each time he moved the selector to a new position, he left it in the selected position for what he estimated was 15 to 20 seconds. Being unable to restart the engine, and finding no suitable place in which to land, he elected to attempt a forced landing between the stacks of logs in a very small commercial log-sorting yard. During his attempt to land in this small area, the aircraft contacted the terrain with sufficient force to cause one main gear to collapse. In a post-accident telephone conversation, the pilot stated that during his efforts to restart the engine before running out of altitude, he had trouble feeling the fuel selector position detents, and was not sure that he had been able to place the selector accurately. After the accident, the owner and an FAA Airworthiness Inspector inspected the engine and the aircraft fuel system. No engine mechanical discrepancies were noted, and it was determined that although the selector position detents were not easily discernable, the fuel selector valve functioned normally. After further discussions with the inspector, the pilot suggested that it was probable that he did not get the selector in the corrected position both times that he tried to select the left tank, and that he may have initially moved the selector from the right tank to the left tank just as the right tank reached empty.