EMER LNDG AT NON TWR ARPT BY SMA PLT AFTER EXPERIENCING ENG STOPPAGE DUE TO FUEL STARVATION. PLT LOSES ACFT CTL AND HAS A RWY EXCURSION. POSTFLT INSPECTION REVEALED HOLE IN L BRAKE LINE.

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FLT WAS XCOUNTRY FROM BEAUFORT; NC; TO HYDE FIELD; MD; RIGHT OUTSIDE WASHINGTON; DC. FUEL PLANNING SHOWED THAT WE WOULD HAVE 45 MINS OF RESERVE FUEL ON LNDG; SO WE WERE USING A LITTLE OVER 3/4 OF OUR AVAILABLE FUEL. ABOUT 2/3 OF THE WAY THERE; THE L FUEL GAUGE STILL INDICATED FULL AND THE R INDICATED JUST OVER 1/4 OF THE TANK REMAINING SO I SWITCHED THE FUEL SELECTOR VALVE TO L. WE ENTERED THE WASHINGTON TCA -- 20 MINS LATER WHERE WORKLOAD INCREASED DRAMATICALLY ON OUR VFR FLT. WE RECEIVED APCH CTL VECTORS TO THE UNCTLED FIELD AND SWITCHED TO UNICOM FREQ. I ENTERED THE LNDG PATTERN DIRECTLY OVER THE DUTY RWY 500 FT ABOVE PATTERN ALT AND BEGAN MY DSCNT AT THE UPWIND NUMBERS. AT 1200 FT MSL (FIELD ELEVATION 49 FT) THE ENG FLAMED OUT WITH NO WARNING AT ALL. I GLIDED AROUND THE PATTERN; DECLARING MY INTENTIONS AND SITUATION ON UNICOM FREQ. I WENT THROUGH THE LNDG CHKLIST BUT SKIPPED THE FUEL SELECTOR. I FLEW THE PATTERN TOO TIGHT AND ENDED UP TURNING TO FINAL IN 60 DEG ANGLE OF BANK ABOUT 50 FT OVER 2 AIRPLANES IN THE HOLD SHORT AREA. I LANDED ON THE RWY TO DISCOVER THAT THE L BRAKE WAS INOP AND WAS UNABLE TO CORRECT R DRIFT ON RWY AND RAN OFF THE EDGE INTO THE GRASS WITH NO DAMAGE TO THE ACFT OR THE ARPT PROPERTY. POST-FLT INSPECTION REVEALED HOLE IN L BRAKE LINE AND L TANK DRY AND ABOUT 10 GALLONS N R TANK. L FUEL INDICATOR SHOWED 3/4 FULL AND R SHOWED JUST UNDER 1/4 REMAINING. THIS HIGH WING SMA ACFT NEEDS BETTER FUEL GAUGES. I NEED TO DO BETTER LNDG CHKS AND I WILL NEVER AGAIN USE THE FUEL SELECTOR VALVE; REGARDLESS OF FUEL INDICATIONS.