THE COMMERCIAL PILOT HAD INITIATED A DIVERT TO ANOTHER AIRPORT AFTER HEARING REPORTS OF LOW VISIBILITIY AT HIS DESTINATION. HE REPORTED THAT HE HAD NO APPROACH PLATES FOR HIS DIVERT FIELD. WHILE BEING RADAR VECTORED AT ABOUT 3,000 FEET AGL, HE REPORTED 'HAVING ENGINE PROBLEMS.' ABOUT 1 MINUTE LATER, HE REPORTED 'GOING DOWN'. THE AIRCRAFT CRASHED IN WOODED TERRAIN AND BURNED. THE DESCENT ANGLE THROUGH THE TREES WAS ABOUT 30 DEGREES. RADAR DATA INDICATES THAT THE AIRCRAFT RAPIDLY LOST ABOUT 30 KNOTS PRIOR TO THE PILOT'S LAST RADIO CALL, FOLLOWED BY A HIGH RATE OF DESCENT. AN EXAMINATION OF THE WRECKAGE REVEALED THAT THE LEFT PROPELLER WAS NEAR THE FEATHERED POSITION AT IMPACT. THERE WAS EVIDENCE OF POWER ON THE RIGHT ENGINE AT IMPACT. TEARDOWNS OF BOTH ENGINES AND THEIR COMPONENTS FAILED TO EXPLAIN THE REPORTED ENGINE PROBLEM.