ATX PLT GETS FLT ASSIST TO LAND AT ALTERNATE ARPT ON EMER DIVERSION AFTER FUEL EXHAUSTION LEADS TO AN INFLT ENG SHUTDOWN.

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DISPATCH ADVISED ME THAT A TRIP WAS SCHEDULED FROM RST TO CVX TO DEPART AM00 ON SEP/SUN/91 FOR A PICK UP OF A PAX AND FAMILY MEMBER AT CVX. I LOADED FUEL TO APPROX 550 POUNDS PER SIDE WITH A TOTAL FUEL LOAD OF APPROX 1100 POUNDS. THIS WAS WITHIN WT AND BAL OF THE ENVELOPE ON THE ACFT AND FOR THE TRIP AND PAX INVOLVED. THE TRIP DEPARTED RST AT AM55 LCL TIME. CLB WAS TO 9000 AND TOOK APPROX 8 MINS. CRUISE WAS SET AT 105 POUNDS FUEL FLOW PER SIDE. ENRTE TO CVX IT WAS NOTED THAT THE R FUEL QUANTITY GAUGE HAD SPIKED TO THE TOP OF THE STOP. MANIPULATION OF THE CIRCUIT BREAKER DID NOT SHOW ANY CHANGE. WHEN THE CIRCUIT BREAKER WAS DISCONNECTED; THE DISPLAY NEEDLE DROPPED TO 0. WHEN THE CIRCUIT BREAKER WAS RECONNECTED; IT SPIKED. IT WAS LEFT IN THE SPIKED POS WITH THE CIRCUIT BREAKER BEING CHKED FROM TIME TO TIME DURING THE COURSE OF THE TRIP TO SEE IF THE SITUATION WOULD CORRECT ITSELF. IT DID NOT. ARR AT CVX WAS UNEVENTFUL AND 9 GALLONS OF FUEL WERE PUT IN EACH SIDE. DEPARTED CVX AT APPROX PM15 LCL TIME AND ALL SYS APPEARED TO OPERATE NORMAL. DURING CLB THROUGH 4000 FOR ASSIGNED ALT OF 8000; IT WAS NOTED THAT THE R FUEL PRESSURE HAD DROPPED TO A SETTING WHICH APPEARED AS THE 'LOW' SETTING FOR THE LOW FUEL PRESSURE. THE SWITCH WAS PLACED IN THE 'HIGH' SETTING FOR HIGH FUEL BOOST. THE L SIDE WAS NORMAL. AT THAT TIME; BOTH FUEL BOOST PUMPS WERE PLACED IN THE 'LOW' SETTING WITH NO APPARENT REDUCTION ON THE R SIDE BUT WITH THE NORMAL REDUCTION ON THE L SIDE. LEVELING OFF BOOST PUMPS WERE L IN THE 'LOW' SETTING AND FUEL FLOW WAS ADJUSTED TO SLIGHTLY OVER 100 POUNDS PER HR PER SIDE. THERE WAS NO CHANGE IN THE FUEL QUANTITY READING (I.E.; IT WAS AT THE STOP AT GREATER THAN 600 POUNDS) ON THE R SIDE. AGAIN; ATTEMPTS AT RESETTING AND PULLING THE CIRCUIT BREAKER GAVE NO CHANGE. THE FLT CONTINUED UNEVENTFULLY. AT APPROX 1 HR AND 15 MINS OUT OF CVX; IT WAS NOTED THAT A LOW FUEL LIGHT APPEARED ON THE ENUNCIATOR PANEL. I FLEW APPROX 10 MORE MINS AND TURNED ON THE FUEL TRANSFER PUMP. THE FUEL QUANTITY GAUGE ON THE L SIDE INDICATED CLOSE TO 300 POUNDS OF FUEL REMAINING. ESTIMATED TIME TO RST WAS 1 HR AND 5 MINS. BOTH BLUE LIGHTS ON THE FUEL TRANSFER PUMP WERE OPERATING. APPROX 10 MINS LATER; THE FUEL PRESSURE DROPPED ON THE R ENG TO LESS THAN 30 POUNDS OF FUEL FLOW. THE FUEL FLOW FLUCTUATED TO 0 AND BACK AND THEN OFF AGAIN. THE MANIFOLD PRESSURE ON THE R ENG DROPPED TO BELOW 25 INCHES. THE R FUEL BOOST WAS PLACED ON HIGH WITH NO EFFECT. THE R THROTTLE WAS PLACED ON FULL FORWARD WITH NO EFFECT. FULL PROP AND FULL RICH MIXTURE ALSO WITH NO EFFECT. R FUEL BOOST WAS TURNED OFF WITH XFEED TURNED ON AND L FUEL BOOST ON HIGH. NOTHING HAPPENED. THE R ENG APPEARED TO DEFINITELY HAVE LOST PWR; AND UPON VERIFICATION THE SHUTDOWN PROC WAS COMPLETED AND THE R ENG WAS FEATHERED. I ASKED FOR VECTORS FROM ATC TO LSE FOR THE ILS. I HAD ALREADY OBTAINED WX AT LSE AND HAD THE APCH PLATE FOR USE. THEREAFTER; AFTER VECTORS TO THE FINAL APCH COURSE FOR LSE; A SINGLE ENG UNEVENTFUL APCH AND LNDG WAS COMPLETED. THE PAX DEPLANED AND A CALL WAS MADE TO RST AVIATION DESCRIBING THE PROBLEM. I THINK I SHOULD NOT HAVE DEPARTED WITH THE FUEL QUANTITY DISPLAY INOP.