PLT OF A C310 LOST CTL OF THE ACFT WHILE TAXIING OUT FOR TKOF. CAUSED BY L MAIN WHEEL BRAKE FAILURE RESULTING IN GOING OFF THE SIDE OF THE TXWY. THE PLT RECOVERED CTL AND TAXIED BACK ONTO THE TXWY AND SUBSEQUENTLY; UNDER TWR CTL; REPOSITIONED THE ACFT OUT OF THE WAY OF OTHER TFC TO WAIT FOR A TOW BACK TO THE HANGAR.

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ACFT WAS TAXIING TO THE ACTIVE. I BEGAN BRAKING APPROX 200 YARDS FROM THE END OF THE TXWY TO TEST THE BRAKES AND THE STOPPING DISTANCE. PRIOR BRAKE TEST BEFORE INITIAL TAXI WAS SUCCESSFUL AND BRAKES APPEARED TO WORK FINE. AFTER THE TEST THE ACFT APCHED THE END OF THE TXWY; I APPLIED FULL BRAKE PRESSURE BUT THE ACFT WOULDN'T STOP. THE ACFT EXITED THE TXWY FOR A FEW FEET WHEN I APPLIED ASYMMETRIC PWR AND THE ACFT RETURNED TO THE TXWY. R BRAKE WAS OPERABLE. I WAS UNABLE TO RETURN TO THE HANGAR VIA THE TXWY BECAUSE A L TURN WAS IMPOSSIBLE EVEN WITH ASYMMETRIC THRUST. SO I CALLED TWR; ALERTED THEM OF MY SIT AND ASKED TO TAXI DOWN THE RWY. I MADE IT DOWN THE RWY BUT COULD NOT MAKE THE INTXN TWR INSTRUCTED ME TO MAKE FOR 2 REASONS: 1) I COULDN'T TURN L HARD ENOUGH TO MAKE THE INTXN. 2) THERE WAS A CESSNA BLOCKING THE INTXN THAT I WOULD BE CERTAIN TO HIT IF I HAD EVEN MADE THE TURN. SO I CONTINUED STRAIGHT AHEAD; TOLD TWR THAT I WAS GOING TO MAKE A R 270 DEG TURN TO CLR THE RWY. I SUCCESSFULLY CLRED THE RWY; CALLED TWR TO GET A TUG OUT TO US AND I SECURED THE ACFT.