THE PLT & 3 PASSENGERS TOOK OFF AT NIGHT ON AN OVER WATER FLT TO AN ISLAND IN LAKE ERIE TO PROVIDE HELP TO A HEART PATIENT. NO FLT PLAN WAS FILED & NO RECORD OF A WX BRIEFING WAS FOUND. REPORTEDLY, AFTER TAKEOFF, THE ACFT DISAPPEARED IN A CLOUD OR HAZE. ALSO AFTER DEPARTING, SHERIFF'S PERSONNEL RECEIVED A RADIO CALL FROM THE ACFT STATING 'WE ARE IN IT.' ACCORDING TO LOCAL RESIDENTS, THERE WAS PATCHY FOG IN THE AREA. WHEN THE ACFT DID NOT ARRIVE AT ITS DESTINATION, A SEARCH WAS INITIATED. THE PLANE WAS FOUND IN LAKE ERIE ALONG THE EXPECTED ROUTE OF FLT. THE ACFT WAS INTACT, EXCEPT THE ENG WAS LOOSE FROM THE FIREWALL & THERE WAS MAJOR DAMAGE TO THE RIGHT, OUTER WING PANEL. NO PREIMPACT/MECHANICAL MALFUNCTION/FAILURE WAS FOUND. ABOUT 45 MI WEST AT TOLEDO, OH, THE 2150 WX IN PART WAS: 1500 FT OVERCAST, VISIBILITY VARIABLE 1 TO 2 MI WITH FOG, TEMP 32, DEW POINT 31, WIND FROM 330 DEG AT 4 KTS.