THE PILOT REPORTED THAT DURING THE PREFLIGHT OF HIS FLOATPLANE HE VISUALLY CHECKED INSIDE THE FUEL TANKS AND ESTIMATED THAT HE HAD 12 TO 15 GALLONS OF FUEL. HE THEN DEPARTED WITH THE INTENTION OF FLYING TO A NEARBY SEAPLANE BASE APPROXIMATELY 12 NAUTICAL MILES NORTHWEST WHERE HE PLANNED TO PURCHASE FUEL. DURING THE INITIAL CLIMB AND AT AN ALTITUDE OF APPROXIMATELY 300 TO 400 FEET AGL THE ENGINE QUIT AND THE PILOT EXECUTED A FORCED LANDING TO THE LAKE SURFACE. DURING HIS DESCENT HE ENTERED AN AREA OF FOG AND DUE TO REDUCED VISIBILITY HE 'COULD NOT JUDGE WHEN TO FLARE' AND A HARD LANDING FOLLOWED. THE FUEL SYSTEM LINES WERE FOUND TO BE INTEGRAL WITHOUT BREACHES, AND AIRCRAFT RECOVERY PERSONAL REPORTED THAT SHORTLY AFTER THE ACCIDENT, WHILE THE WINGS WERE BEING REMOVED, THEY FOUND NO FUEL IN EITHER FUEL BLADDER. SUBSEQUENT TO THE AIRCRAFT'S RECOVERY TO A NEARBY AIRPORT, TOTAL FUEL AMOUNTS OF 6 OUNCES, 1 OUNCE, AND LESS THAN ONE OUNCE WERE DRAINED RESPECTIVELY FROM THE LOW POINT FUEL FILTER, FUEL LINE LINKING THE BOOST PUMP TO THE ENGINE, AND FROM THE HEADER TANK LOW POINT DRAIN.