PLT OF AN SMT ATX ACFT HAD AN ENG QUIT DURING ENRTE CRUISE DUE TO FUEL STARVATION.

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ON THE MORNING OF MAR/WED/94; I WAS ACTING AS PIC FOR A SINGLE PLT FLT IN A BEECHCRAFT BARON (BE58) THAT WAS ON A CHARTER FLT FROM RALEIGH; NC; TO CHARLESTON; WV. IN PREPARATION FOR THIS FLT; THE CALCULATIONS FOR ACFT WT AND BAL INDICATED THAT A MAX FUEL LOAD COULD NOT BE GREATER THAN APPROX 90 GALLONS. THE PROC USED FOR FUEL LOAD COMPUTATION ON THIS ACFT (1973 BE58) IS TO RECORD THE GALLONS LOADED IN A DAILY ACFT LOG AND COMPARE FUEL LOAD TO HRS FLOWN TO DETERMINE FUEL REMAINING AT THE END OF EACH FLT. THE ACFT FUEL GAUGES ARE NOT PRESENTLY USED AS AN ACCURATE INDICATOR OF ACTUAL FUEL LOAD. BASED ON THIS DATA; I DETERMINED THAT THE ACFT HAD APPROX 90 GALLONS OF FUEL ON BOARD. THE PAX WERE LOADED AND THE FLT DEPARTED RDU AT APPROX XA30. THIS FLT WAS FORECASTED TO BE FLOWN MOSTLY IMC. WHILE IN IMC AT 6000 FT MSL; APPROX 45 MINS INTO THE FLT; THE L ENG BEGAN TO SPUTTER/SURGE AND THE FUEL PRESSURE GAUGE BEGAN TO FLUCTUATE. FOLLOWING CHKLIST PROCS; I TURNED ON THE FUEL BOOST PUMP BUT THE PROB DID NOT CORRECT ITSELF. I DID NOT SUSPECT FUEL STARVATION BUT DID NOT LEAVE OUT THIS POSSIBILITY. I SUSPECTED BLOCKAGE OR CONTAMINATION. I IMMEDIATELY REQUESTED ATC ASSISTANCE FOR VECTORS TO THE NEAREST ARPT (ROA) WHICH WAS APPROX 20 NM TO THE E OF MY POS. ATC CLRED ME TO DSND TO 4000 FT MSL. WHILE ON MY ASSIGNED HDG AND DSNDING TO 4000 FT; THE L ENG QUIT RUNNING. I DETERMINED THAT THE BEST REACTION WOULD BE TO CONSERVE FUEL IF THIS WAS; IN FACT; THE PROB. I FEATHERED THE L ENG TO OBTAIN BEST PERFORMANCE AND TO CONSERVE FUEL. I WAS IMC WITH MODERATE TO SEVERE TURB CONDITIONS. I EXTENDED THE LNDG GEAR TO ASSIST IN STABILIZING THE ACFT WHILE CONTINUING TO ATTEMPT TO MAINTAIN ASSIGNED ATC HDGS AND ALTS. I DISCOVERED THAT I WAS NOT ABLE TO MAINTAIN 4000 FT MSL AND KEEP THE ACFT AT OR ABOVE VMC DUE TO THE TURB. I INFORMED ATC THAT I WOULD NEED TO CONTINUE DSNDING. ATC VECTORED ME AWAY FROM MOUNTAINOUS OBSTRUCTIONS AND I CONTINUED TO DSND TO APPROX 3000 FT MSL. ATC THEN VECTORED ME TOWARDS THE ROANOKE ARPT. I WAS NOW OUT OF THE TURBULENT CONDITIONS. I RAISED THE LNDG GEAR AND MAINTAINED APPROX 2700 FT MSL UNTIL VISUAL CONTACT WAS MADE WITH ROANOKE ARPT. I WAS CLRED FOR AN IMMEDIATE VISUAL APCH TO RWY 33 AND LANDED WITHOUT FURTHER INCIDENT. I FOLLOWED OUR OP SPECS PROCS AND CONTACTED OUR DIRECTOR OF MAINT TO RPT THE PROB. HE STATED THAT I SHOULD CHK FOR ANY FUEL CONTAMINANTS; CHK FOR ANY LOOSE COMPONENTS THAT MAY BE VISIBLE THROUGH ENG COWLING OPENINGS; AND TRY TO DETERMINE IF FUEL STARVATION MAY HAVE OCCURRED TO THE L ENG. I HAD NO WAY TO DETERMINE THE EXACT CONTENTS OF THE FUEL TANKS. THERE IS NO VISUAL WAY TO INSPECT THE FUEL LOAD OF THIS MODEL OF BEECH BARON EXCEPT WHEN FUEL IS FULL. I DRAINED SOME REMAINING FUEL OUT OF THE L WING FUEL SUMPS AND DID NOT SEE ANY CONTAMINATION. I VISUALLY INSPECTED THE ENG COMPONENTS THROUGH THE COWLING OPENINGS. NO VISUAL INDICATION OF A PROB WAS APPARENT TO ME. I SUSPECTED FUEL STARVATION HAD OCCURRED. I LOADED ADDITIONAL FUEL INTO BOTH ACFT WING TANKS. I DRAINED THE FUEL SUMPS TO TEST FOR CONTAMINANTS; ONLY A SMALL AMOUNT OF WATER WAS FOUND. I STARTED THE R ENG. IT OPERATED NORMALLY. I STARTED THE L ENG. IT ALSO APPEARED TO OPERATE NORMALLY. I PERFORMED A LENGTHY WARM- UP AND THEN FOLLOWED CHKLIST PROCS FOR CHKING THE OP OF A TEST FLT WITHIN THE ROANOKE ARPT AREA. NO PROBS WERE FOUND. I LANDED AND PERFORMED ANOTHER THOROUGH OP CHK ON THE ENGS -- NO PROB WAS FOUND. I VISUALLY INSPECTED THE ENG AND FUEL ONE MORE TIME -- NO PROBS WERE APPARENT. I DETERMINED THAT FUEL STARVATION WAS THE MOST PROBABLE CAUSE. I DECIDED THAT THE FLT COULD CONTINUE TO OUR SCHEDULE DEST. WE DEPARTED ROANOKE AND FLEW TO CHARLESTON; WV; WITHOUT FURTHER INCIDENT. FUEL STARVATION TO L ENG. PLT JUDGEMENT THAT RECORDED FUEL LOAD ADDITIONS AS COMPARED TO RECORDED FUEL CONSUMPTION WERE PROVIDING ACCURATE REMAINING FUEL BAL. INACCURATE FUEL QUANTITY GAUGE READINGS. NO METHOD TO VISUALLY INSPECT FUEL QUANTITY IN TANKS ON THIS YR OF BEECH BARON.