B767-200 ACFT ON STAR ARR HAD COM PROBS CONTACTING APCH CTLR AND WHEN FINALLY ESTABLISHING COM THE FLC WAS INFORMED THEY WERE OFF COURSE. AFTER CHKING NAV ACCURACY THEY FOUND ALL 3 INERTIAL REF UNITS OUT OF TOLERANCE (60 MI OFF). ATC VECTORED ACFT FOR APCH AND LNDG.

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PROCEEDING DIRECT CARTR WHILE DSNDING ON THE ARR TO SLC IN B767-200; FO FLYING WITH AUTOPLT ON; LNAV AND VNAV ENGAGED. JUST FELT FMS WAS NOT GIVING US CORRECT POS FROM CARTR. XCHKED ON FIX PAGE AND MANUAL VOR -- OGD RADIAL. ALL CHKED OK ON MAP. WHEN CALLED APCH TO VERIFY; NO ANSWER. MADE 3 CALLS; STILL NO ANSWER. FINALLY SWITCHED TO TWR AND INSTRUCTED TO RETURN TO FREQ WE WERE ORIGINALLY ON. APCH ANSWERED WE HAD PASSED CARTR BY 20 MI (W). INFORMED APCH FMS HAD BECOME INACCURATE -- CHANGE TYPE ACFT -- NEEDED VECTORS. ON FINAL TO RWY 16R; I EXTENDED RWY ON FMS AND AT TOUCHDOWN WE SHOWED 62 MI FROM RWY. DISCOVERED ALL 3 INERTIAL REF UNITS OVER 1 DEG E OF CORRECT POS. XCHKED GATE POS AT BOSTON (OUR STARTING POINT) -- ITS LATITUDE/LONGITUDE WAS CORRECT. I ALSO CHKED ACFT POS ON MAP AS WE TURNED TO ACTIVE RWY -- SHOWED US ON RWY 22R (BOS). THIS TURNED OUT FINE BECAUSE WE VISUALLY FELT UNCOMFORTABLE. (BY LOOKING AT THE VARIOUS VALLEYS WE THOUGHT CARTR WAS IN.) IF IMC; WOULD HAVE DRIVEN EXTRA 25 MI TO CARTR FAT; DUMB; AND BLIND. STILL DON'T UNDERSTAND WHAT HAPPENED TO APCH CTL ON THE RADIO. MUST HAVE BEEN IN BLIND SPOT? WE TRUST THE MAGIC SO MUCH -- WE HAD NO CLUES. ONE PLT COULD HAVE BEEN IN MANUAL TO VERIFY XING RADIALS FROM OGDEN BUT WHO THOUGHT ALL 3 INERTIAL REF UNITS COULD GET LOST ON LONGITUDE ONLY; LATITUDE WAS CORRECT. NO FMC MESSAGE. IT'S AN EYE OPENER!