JUST PRIOR TO THIS FLT, THE PLT HAD FLOWN FROM HORNELL, NY TO WELLSVILLE, NY. BEFORE DEPARTING HORNELL, HE RADIOED THAT THE VACUUM ANNUNCIATOR LIGHT WAS ON, & DURING A RUN-UP, THE SUCTION GAUGE READ ZERO. GROUND PERSONNEL ADVISED THAT WITH THIS PROBLEM, THE ARTIFICIAL HORIZON, DIRECTIONAL GYRO & AUTOPILOT WOULD BE INOP & TO STAY AWAY FROM CLOUDS. AFTER LANDING AT WELLSVILLE, PASSENGERS ENPLANED WHILE THE ENG WAS RUNNING. THE ACFT DEPARTED WELLSVILLE AT APRX 0925 IN WX ESTIMATED TO BE 900 FT OVERCAST, VISIBILITY 1 1/2 TO 2 MI. APRX 10 MIN LATER, IT CRASHED & BURNED AFTER HITTING TREES ONRISING TERRAIN, APRX 7 MI ESE OF THE ARPT. IT IMPACTED ON A HEADING OF 240 DEG. PRIOR TO IMPACT, WITNESSES NEARBY HEARD AN AIRCRAFT TRAVELING GENERALLY FROM WEST TO EAST THAT SOUNDED LOUD & LOW. ONE STATED HE COULD NOT SEE THE ACFT DUE TO DENSE FOG. THE NON-INSTRUMENT RATED PLT HAD RECEIVED DUAL INSTRUMENT TRAINING, BUT VERY LITTLE PARTIAL PANEL TRAINING. AN EXAM OF THE VACUUM PUMP REVEALED THE DRIVE SHAFT WAS SHEARED.