THE PLT LISTED A TOTAL FUEL ENDURANCE OF 5+30 ON HIS FLT PLAN & A TOTAL OF 182 GALS AT TAKEOFF ON HIS PLT/OPERATOR ACCIDENT REPORT. THE TOTAL ACFT FUEL CAPACITY IS 162 GALS. THE FLT DEPARTED A 1055. AT 1527 THE PLT RECEIVED DESTINATIONWX OF CEILING INDEFINITE 100 FT SKY OBSCURED VISIBILITY 1/8 MI IN FOG. THE PLT STATED HE UNDERSTOOD THE VISIBILITY AS 18 MI & SHOT AN APPROACH TO JOHNSON COUNTY EXEC ARPT. AT 1532 HE DECLARED A MISSED APCH & ADVISED KANSAS CITY APPROACH HE WAS LOW ON FUEL. HE WAS CLEARED FOR AN APPROACH TO KANSAS CITY INTL ARPT. AT 1541 THE PLT ADVISED THAT BOTH ENGS HAD FAILED. THE ACFT IMPACTED THE GROUND ABOUT 1 MI SHORT OFTHE ARPT. THERE IS NO EVIDENCE THAT THE PLT OBTAINED ENROUTE WX BRIEFINGS FOR WX CONDITIONS AT JOHNSON COUNTY EXEC ARPT. WX OBSERVATIONS AT & AFTER 0754 REPORTED WX BELOW THE LANDING MINIMUM REQUIRED FOR AN INSTRUMENT APCH TO THE ARPT. THERE WAS NO EVIDENCE OF FUEL FOUND IN ANY OF THE ACFT'S FIVE FUEL TANKS.