Prior to departing on the cross-country flight, the pilot received a jump-start for his amphibious airplane due to a dead battery. The pilot then immediately taxied to the runway and departed. Once airborne, he moved the landing gear handle to the "Up" position, but did not confirm that the gear had successfully retracted. He climbed to 300 feet above mean sea level (msl) before turning and descending over the water to 120 feet msl, with the intention of making a low pass in front of his waterfront home. The airplane encountered "a gust of wind," and lost approximately 40 feet of altitude. The pilot decided to abort the low pass, and advanced the throttle to full power. He was not satisfied with the response of the engine and decided to make an emergency landing on the water. Upon touchdown, the airplane flipped over, and sustained substantial damage. The pilot escaped underwater and received minor injuries. Examination of the wreckage revealed that the landing gear was in the extended position, and the gear handle was in the "Up" position. All electrical wiring was found to be intact, and no other mechanical issues were found. A certificated aircraft mechanic, familiar with the accident airplane, stated that when the landing gear cycle was initiated, the motor momentarily drew a very high current. He stated that if the battery was dead, or contained a low charge, the generator would "probably not" be able to handle the high current demand, and would not permit the landing gear to cycle. The pilot did not notice any other mechanical or electrical problems with the airplane during the flight.