PA28 INSTRUCTOR AND STUDENT LAND WITHOUT CLRNC DUE TO DISTRACTION CAUSED BY SUSPECT BRAKE EFFECTIVENESS AT A HIGH ALT ARPT.

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WHILE APCHING GCN ON THE ILS TO RWY 3; I WAS INSTRUCTED TO CONTACT TWR BY ZLA. MY CONTACT WITH THE TWR WAS ACKNOWLEDGED ONLY. AT 3 MI I CONTACTED THE TWR AGAIN RPTING OUR POS ON THE APCH. MY STUDENT NOTICED AT THIS TIME THAT THE BRAKES WERE QUITE SOFT. TWR ASKED OUR INTENTIONS AND; AS WINDS FAVORED RWY 21; I REQUESTED CIRCLING AND FULL STOP. TWR INSTRUCTED THAT WE 'CIRCLE W TO R BASE RWY 21.' THE INSTRUCTION WAS READ BACK. WHILE CIRCLING; MY STUDENT AND I DISCUSSED THE SAFEST POSSIBLE WAY TO LAND IN THE EVENT OF ZERO BRAKING EFFECTIVENESS. STRATEGIES WERE DISCUSSED AND A PLAN WAS DECIDED UPON TO LAND JUST SHORT OF THE 'BLOCKS.' A NORMAL FINAL WAS MADE; HOWEVER; MY STUDENT DID INDICATE THAT MORE PWR WAS NEEDED THAN NORMAL. AFTER TOUCHDOWN; ON ROLLOUT; THE ENG QUIT. RESTART WAS UNSUCCESSFUL AND WE REQUIRED A TOW TO PARKING. I WAS ASKED TO CALL THE TWR. WHILE TALKING TO THE TWR CTLR; I WAS INFORMED THAT WE HAD NOT RECEIVED A LNDG CLRNC. THERE WAS NO OTHER TFC IN THE AREA WHEN WE LANDED. I BELIEVE THE TWR SHOULD ISSUE LNDG CLRNC TO ACFT ON DOWNWIND OR 2-3 MI FINAL -- NOT; AS THE CTLR TOLD ME; ON BASE. WITH OUR ABNORMAL SITUATION (BRAKES); WE BECAME TOO BUSY IN THE BASE AND FINAL APCH PHASE AND THE TWR DID NOT KNOW OR TRACK OUR POS. BOTH FACTORS CONTRIBUTED TO A LNDG WITHOUT CLRNC.