THE FLT DEPARTED HONOLULU WITH RADAR FLIGHT FOLLOWING TO THE THE LIMIT OF THE TCA; THE LAST RADIO COMMUNICATION WAS AT ABOUT 0850 HRS. FOR THE NEXT APRX ONE HOUR, RECORDED RADAR DATA SHOWS THE AIRPLANE N AND E OF MOLOKAI AND MAUI AT ALTITUDES VARYING FROM 100 FT TO 13,600 FT BEFORE DISAPPEARING FROM RADAR. THE LAST POSITION WAS ABOUT 45 MI N OF MAUI IN THE PACIFIC OCEAN. PILOTS FLYING IN THE GENERAL VICINITY OF LANAI, MOLOKAI AND MAUI ISLANDS REPORTED ENCOUNTERING LOWERING CEILINGS & VISIBILITIES AS THEY PROGRESSED E FROM HONOLULU, WITH IFR CONDITIONS IN THE AREA OF LANAI. WEATHER FORECASTS FOR LOCATIONS W AND E OF THE ACCIDENT AREA WERE FOR MARGINAL VFR CONDITIONS. THE 0945 WEATHER AT MOLOKAI WAS 300 FT SCATTERED, 1,000 FT OVERCAST, AND VISIBILITY 1-1/2 MI IN RAIN AND FOG. A NEARLY STATIONARY FRONTAL SYSTEM WAS LOCATED JUST W OF KAUI. THE AIRPLANE WAS NOT RECOVERED; DAMAGE AND INJURIES ARE PRESUMED.