C172 FLIGHT INSTRUCTOR REPORTS CFIT DURING ATTEMPTED LDA-C APPROACH INTO EKN.

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ENRTE; WE JOINED THE CKB TRANSITION R-133 OF CKB TO THE LDA-C INTO EKN. WE WERE AT 5000 FT MSL AND IN AND OUT TO THE TOPS OF SOME CLOUDS WITH LITTLE REF TO THE GND. CDB APCH CALLED US AND TOLD US TO RPT THE FIELD IN SIGHT. I REPLIED WE WERE EXPECTING TO SHOOT THE LDA-C. THE CTLR INDICATED HE THOUGHT THAT APCH WAS NO LONGER CERTIFIED. I REPLIED WE HAD CURRENT CHARTS FOR IT AND HE INDICATED THAT HE THOUGHT IT WAS NOTAMED OUT THAT IT WASN'T A RELIABLE APCH. HE INDICATED HE WAS GOING TO DOUBLE-CHK THE NOTAMS; CLRED US TO FLY THE LOC ON THE LDA BUT TO NOT DSND BELOW 5000 FT. HAVING SHOT THE APCH EARLIER IN THE WK; AND HAVING CHKED NOTAMS AND NOT SEEING A NOTAM THAT HAD THE LDA OTS; I THOUGHT THE NOTAMS HE WAS REFERRING TO WERE THE ONES THAT INDICATED THAT THE COURSE WAS ONLY USABLE 25 DEGS; BEYOND THAT L AND R WOULDN'T SHOW INDICATION; AND THE 2 OTHER NOTAMS THAT WERE ON THE LIMITS OF THE DME (7/052 7/042 AND 7/40). THE NAV #1 WAS SET TO CKB AND TRACKING THE 133 DEG RADIAL. NAV #2 SET TO THE LOC OF THE LDA BUT HAD NAV FLAG. DME SET TO LOC DISTANCE SHOWED AT 9 MI AND WOULD POP IN AND OUT. ADF WAS SET TO RQY AND WITH CORRECT IDENT AND POINTING SLIGHTLY TO THE R OF OUR NOSE BUT WOULD SWING ABOUT 30 DEGS TO R OF OUR NOSE AT TIMES. MARKER BEACONS WERE SET TO LOW AND TEST SHOWED ALL LIGHTS WORKING. I MADE A MENTAL NOTE THAT IF WE DIDN'T PICK UP THE LOC BY 200 BEARING OF THE NDB OR MARKER BEACONS THAT I WOULD CALL ATC FOR VECTOR BECAUSE WE WERE NOT PICKING UP THE LOC. IN IMC ABOUT 75% OF THE TIME NOW WHEN WE POP OUT I LOOK FOR SOME GND TO GET REF TO OUR SITUATION BUT NEVER SAW PASSING OVER THE FIRST SET OF MOUNTAINS TO INDICATE WE WERE IN THE VALLEY AREA OF THE APCH. NEXT I HEAR ATC GIVING US AN INSTRUCTION TO IMMEDIATELY CLB TO 6000 FT; MY STUDENT STARTS EXECUTING THE CLB AS HE READS THE INSTRUCTION BACK. I HEAR THE CTLR AGAIN ISSUING AN IMMEDIATE CLB TO 6000 FT AND R TURN TO 270 DEGS AND REPLY. MY STUDENT STARTS TO TURN L; I TAKE CTL AND EXECUTE A CHANDELLE TO THE R AS WE POP OUT OF THE TOPS OF THE CLOUDS AROUND 5700 FT AND START LEVELING OFF AT 6000 FT 270. AS I AM DOING THIS THE CTLR IS ASKING US TO IDENT; WHICH I DO. THE CTLR IS NOW TELLING US WE ARE WAY E OF COURSE AND THERE ARE MOUNTAINS AT 5000 FT IN THIS AREA. AS WE ARE BEING VECTORED AND I DOUBLE-CHK MY PLATES AND FREQS I HAD DIALED IN AND THEY WERE ALL CORRECT. ADF NEVER DID SWING MORE THAN 30 DEGS TO THE R; MARKER BEACONS NEVER WENT OFF; AND LOC WAS NEVER PICKED UP. I WENT TO SWING THE NEEDLE ON TEST WITH THE ADF AND IT WOULD NEVER TRY AGAIN TO PICK UP THE STATION AFTER IT WAS MOVED; THOUGH GIVING PROPER IDENT. AFTER LNDG I CHKED THE FAA'S WEB SITE AND SAW NO NOTAM PUTTING THE LDA-C OTS. AFTER GETTING HOME I LOGGED ON TO DUATS AND CHKED AGAIN AND SAW NO NOTAM THERE PUTTING THE LDA-C OTS EITHER. I SAW NO NOTAM BEFORE OR AFTER THE FLT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE ADF WAS DETERMINED TO BE DEFECTIVE AND WAS WRITTEN UP FOR REPAIR; BUT THE REASON FOR THE LOC AND DME PROBLEMS COULD NOT BE DETERMINED AND SEEMED TO WORK NORMALLY ON THE RETURN FLIGHT. THE TERRAIN ON THE EAST SIDE OF EKN IS ABOVE 5000 FEET AND THE CONTROLLER MAY HAVE SAVED THEIR LIVES.