B737-400 CREW GROUND THROUGH 13 TIRE PLIES ON A LNDG AT KTN WITH THE ANTI-SKID MEL'ED INOP.

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WE DEPARTED SMF FOR SEA ON JUN/SUN/03; FLT AB; ACFT X. WHEN THE GEAR WAS RETRACTED; THE 'ANTI-SKID INOP' LIGHT CAME ON. THE LIGHT WENT OUT PASSING FL280 AND STAYED OUT FOR THE REMAINDER OF THE FLT. WE ENTERED THIS INFO IN THE MAINT LOG. IN SEA; MAINT FOLKS TOLD US THAT THE AIRPLANE HAD A HISTORY OF ANTI-SKID PROBS AND THAT THEY WOULD MEL THE ANTI-SKID SYS (MEL 32-2A; I BELIEVE). SINCE WE WERE HEADED TO SE ALASKA; I WAS CONCERNED AND TALKED TO THE DISPATCHER. WE ADDRESSED SEVERAL ISSUES INCLUDING TKOF AND LNDG WTS; TKOF RESTRS; WX; FUEL AND MEL RESTRS. WE AGREED THE FLT COULD SAFELY OPERATE FROM SEA-KTN-JNU. BEFORE PUSHBACK AT SEA; MY FO AND I METHODICALLY REVIEWED THE MEL AND SUGGESTED SECTION OF THE FLT HANDBOOK. WE ALSO WENT THROUGH THE ANTI-SKID INOP WORKSHEET TO MAKE SURE WE WOULDN'T HAVE A VMCG PROB DEPARTING KTN. THE FLT FROM SEA-KTN WAS UNEVENTFUL. WE FLEW THE RNAV APCH RWY 11 AT KTN. THE AIRPLANE WEIGHED ABOUT 105000 LBS. I FLEW A FLAPS 40 DEG APCH AND LNDG. WX WAS ABOUT A 4000 FT CEILING; GOOD VISIBILITY AND WINDS ABOUT 140 DEGS/7 KTS. DUE TO SOME LIGHT TURB OVER THE RWY; I TOUCHED DOWN L MAINS FIRST. THE TOUCHDOWN WAS ABOUT 2000 FT DOWN THE RWY AT TARGET SPD PLUS ABOUT 3 KTS AND ON CTRLINE. SINCE THE SPD BRAKES NEEDED TO BE DEPLOYED MANUALLY; THE AIRPLANE TOOK A MILD BOUNCE ON TOUCHDOWN AND LANDED SMOOTHLY ON BOTH MAINS. I APPLIED THE BRAKES AT ABOUT 100 KTS SEVERAL THOUSAND FT DOWN THE RWY. UNTIL THIS POINT; THE LNDG FELT NORMAL. THE AIRPLANE DECELERATED NORMALLY TO TAXI SPD. AS WE SLOWED TO TAXI SPD; WE COULD TELL WE HAD A FLAT OR SQUARE TIRE. AFTER LNDG; WE DISCOVERED THAT THE L MAIN TIRES HAD BEEN BADLY WORN THROUGH ABOUT 13 PLY. THEY WERE STILL INFLATED; BUT SOMEWHAT DEFORMED. DRIVING OUT TO THE RWY; THE FO SAW SKID MARKS FROM ABOUT 2000-3000 FT DOWN THE RWY JUST L OF CTRLINE. I CALLED MAINT CTL TO SEE IF ANYONE COULD EXPLAIN THE L BRAKE LOCKING UP ON TOUCHDOWN. SUBSEQUENT DISCUSSION WITH THE FLT OPS DUTY OFFICER LED TO THE DECISION TO NOT CONTINUE THE FLT TO JUNEAU; WHERE IT WAS NOW RAINING. WE RECHKED THAT THE ANTI-SKID SWITCH WAS IN THE 'OFF' POS AS PER THE MEL. WE ALSO CONFIRMED THAT THE APCH AND LNDG WAS FLOWN WITH MY HEELS ON THE FLOOR; NOT ON THE BRAKE. THE KTN MAINT PERSON SAID THE SAFETY WIRE ON A SENSOR WAS BROKEN. ACCORDING TO THE CORRECTIVE ACTION IN THE LOGBOOK THE NEXT MORNING; A BOLT IN THE BRAKE SYS HAD SHEARED.