On June 18, 1996, approximately 1915 hours mountain daylight time, a homebuilt Price Berkut, N538AJ, registered to and being flown by a private pilot, was substantially damaged when the landing gear collapsed on landing roll on runway 18 at the Jackson Hole airport, Jackson, Wyoming. The pilot was uninjured. No flight plan was in effect and visual meteorological conditions existed at the time. The flight, which was personal, was to have been operated under 14CFR91, and originated from Sioux City, Iowa, approximately 1500. The pilot reported that approaching the Jackson Hole airport while in turbulence the landing gear "transition" light (indicating hydraulic pump operation) illuminated even though the gear was presumed to be retracted. When the pilot attempted to lower the landing gear they remained retracted. He then manually lowered the gear and the nose landing gear green "down and locked" light illuminated but the corresponding main gear lights did not. The pilot attempted side load maneuvers and high "G" pull-ups to attempt to lock the main landing gear without success and the corresponding main gear green lights remained out. He then executed an approach and landing during which the main landing gear collapsed on rollout and the aircraft impacted several runway light during the subsequent ground slide. The pilot reported in a subsequent telephone conversation that the electrically driven hydraulic motor which operates the landing gear had burned out. Additionally, he reported that the over-center downlock springs which insure the main landing achieving a down-and-locked condition when the hydraulic system has failed, were not installed in the aircraft by the owner/builder from whom he purchased the aircraft. The pilot submitted only pages 1 through 4 of the NTSB Form 6120.1/2 and did not include a narrative history of flight.