C172 PLT AND INSTRUCTOR WENT OFF THE RWY AND HIT A RWY LIGHT AFTER THE L BRAKE FAILED AT A TWR CTLED ARPT.

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I RENTED A C172 ALONG WITH MY INSTRUCTOR. I AM IN THE PROCESS OF GETTING A CHKOUT IN THE ACFT AND A BIANNUAL. I CONDUCTED A PREFLT AND PULLED THE ACFT OUT FOR STARTING. WE NOTICED THAT THE PARKING BRAKE WAS NOT FUNCTIONING IN THE ACFT; BUT DECIDED THAT WE WOULD CONTINUE OUR FLT AND WRITE IT UP AFTER WE RETURNED TO THE HANGAR. WE STARTED THE ENG; LISTENED TO ATIS; AND CONTACTED GND CTL. THEY INSTRUCTED US TO TAXI TO THE RUN-UP PAD LOCATED AT THE N END OF THE ACFT ADJACENT TO RWY. DURING THE RUN-UP IT WAS NECESSARY FOR US TO HOLD THE BRAKES BECAUSE THE PARKING BRAKE DID NOT FUNCTION. AFTER THE RUN-UP; I CONTACTED THE TWR AND NOTIFIED THEM THAT WE WERE READY FOR TKOF. THE TWR INSTRUCTED US TO 'TAXI INTO POS AND HOLD.' I ACKNOWLEDGED THE INSTRUCTION AND PROCEEDED TO TAXI INTO POS. MY INSTRUCTOR STATED THAT HE WAS OFF THE BRAKES. AS WE TAXIED ONTO RWY; I TURNED TO THE R TO CHK FOR LNDG ACFT THAT THE TWR MIGHT NOT KNOW ABOUT. MY INSTRUCTOR MENTIONED THAT THERE WAS AN ACFT ABOUT 3 MI OUT ON FINAL. I TRIED TO STEER THE ACFT TO THE L BUT NOTHING HAPPENED. I PRESSED FIRMLY ON BOTH BRAKES AND PULLED BACK THE THROTTLE. THE ACFT VEERED TO THE R. I MENTIONED TO MY INSTRUCTOR THAT I HAD LOST THE L BRAKE. HE APPLIED PRESSURE ONTO BOTH BRAKES FROM THE R SEAT AND ONLY THE R BRAKE FUNCTIONED. WE BOTH CONTINUED TO PRESS THE BRAKES UNTIL THE ACFT CAME TO REST AT THE APCH END OF RWY. AS THE ACFT WENT OFF THE RWY; I NOTIFIED THE TWR THAT WE HAD LOST OUR L BRAKE AND WERE HAVING DIFFICULTY STEERING THE ACFT. THE ACFT WAS POSITIONED OVER A RED RWY LIGHT. THE RWY LIGHT WAS BROKEN OFF AT THE BASE. AFTER SECURING THE ACFT; I REQUESTED A TUG TO PULL US BACK TO THE HANGAR. WE EXITED THE ACFT AND CHKED THE PROP AND ACFT FUSELAGE FOR OTHER DAMAGE. DUE TO THE HVY TFC; WE GRABBED THE TOW BAR OUT OF THE BAGGAGE COMPARTMENT; PUSHED THE ACFT BACK ONTO THE RWY AND THEN DOWN THE TXWY TO CLR THE RWY. THE TUG ARRIVED AND TOWED US BACK TO THE HANGAR. AT THE HANGAR; WE LOOKED AT THE PROP AGAIN. ONE TIP HS A VERY LIGHT SCRATCH ACROSS THE WHITE PAINT. THE SCRATCH DID NOT PENETRATE THE PAINT. THE OTHER TIP HAD A 3/16-INCH NICK ON THE FACE OF THE BLADE AND 2 INCHES OF THE BLADE TIP WAS BENT AFT ABOUT 1/4 INCH. WHILE REMOVING MY BELONGINGS FROM THE ACFT; I LOOKED AT THE L BRAKE PEDAL AND NOTICED THAT THE PEDAL HAD ROTATED TO A HORIZ POS WITH THE TOP OF THE PEDAL TOWARD THE BULKHEAD. THE NEXT DAY; THE OWNER OF THE ACFT CONTACTED ME. MY INSTRUCTOR AND I MET WITH HIM. HE STATED THAT HE FOUND 8 FT OF BLACK SKID MARK GOING OFF THE RWY AND THAT THE R TIRE HAD FLAT SPOT. HE ADDED THAT THE MECH HAD CHKED THE ACFT AND FOUND NOTHING WRONG WITH THE BRAKES. IN ADDITION; HE ADDED THAT THEY NORMALLY DISCONNECT THE PARKING BRAKE TO SAVE TIRES. HOWEVER; I DON'T RECALL SEEING A PLACARD IN THE ACFT FOR THE PARKING BRAKE. I AM CONCERNED THAT THEY HAD NOT INSPECTED THE L BRAKE THOROUGHLY. THE NEXT TIME THE L BRAKE FAILS; IT MAY RESULT IN A VERY SERIOUS INJURY.