B727 FLC WITH OMEGA NAV ADVISES ATC; LAX APCH; THAT NAV SIGNALS FOR IAP-ILS APCH PROC-STAR ARE NOT BEING RECEIVED. APCH CTLR OFFERS FLT ASSIST; RADAR VECTORING.

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THIS IS AN AUTOMATION-ATC HANDLING PROB. WE WERE ENRTE SLC TO LAX; APPROX 70 MI SW OF MLF WHEN WE WERE CLRED DIRECT TO CIVET; CIVET 1 ARR TO LAX. WE USED OMEGA NAV TO PROCEED DIRECT TO CIVET. ALTHOUGH WE COULD RECEIVE LAX VOR (113.6) WE DID NOT RECEIVE LAX LOC-DME (109.9) AND WERE UNABLE TO ADEQUATELY DEFINE CIVET OR FLY THE ARR (NO DME -- CAN'T MAKE STEPDOWNS; NO LDC -- CAN'T DEFINE INBOUND COURSE). WE INFORMED THE CTLR OF THE SIT AND HE OFFERED US RADAR VECTORS TO A VISUAL FINAL. WE ACCEPTED. OMEGA IS NORMALLY SWITCHED OFF IN THE TERMINAL AREA BECAUSE OF POOR ACCURACY; WE HAD LEFT IT ON AS A BACKUP TO RADAR VECTORS AND THE LAX VOR. WE STARTED RECEIVING LAX DME AT ABOUT 37 DME BUT STILL DID NOT HAVE RELIABLE LOC DATA ON EITHER SIDE OF THE COCKPIT. THE CTLR WORKED WITH US TO BRING US IN LAX. HE DID A FINE JOB. AT APPROX 13 DME ON THE FO SIDE ONLY; OUR ILS LOC DISPLACEMENT BEGAN TO JIVE WITH THE CTLR'S INSTRUCTIONS. THE CTLR OFFERED US THE INBOARD RWY VISUAL APCH. WE ACCEPTED AND DIALED IN THAT ILS FREQ AS WELL. AS I DIALED IN MY ILS; I NOTICED THAT OMEGA WAS STILL SUPPLYING DATA TO MY HSI. I IMMEDIATELY PUSHED THE OMEGA SWITCH LIGHT TO DE-SELECT IT. THE SO THEN STATED; 'WELL; THAT IS THE VERY NEXT ITEM ON OUR APCH CHKLIST.' FLYING INTO THE SUN WHILE LNDG W AT LAX IN THE AFTERNOON; IT WAS DIFFICULT TO SEE THE OMEGA RADIO-NAV SWITCH LIGHT POS IN THE BRIGHT SUNLIGHT. THIS RADIO-NAV SWITCH LIGHT WAS FAR TOO DIM. I WROTE IT UP IN THE ACFT LOGBOOK FOR LAMP REPLACEMENT. THIS SIT COULD HAVE BEEN WORSE. THANK GOODNESS WE HAD INFORMED THE CTLR APCHING CIVET THAT WE HAD INADEQUATE DATA AVAILABLE FOR THE ARR AND WERE ACCEPTING RADAR VECTORS TO THE FIELD WHILE WE TRIED TO WORK OUT WHY OUR DISPLAYS WERE NOT RIGHT. THE FO'S DISPLAY SHOULD HAVE INDICATED OR RECEIVED LAX (109.9) AT LEAST BY CIVET. IT DID NOT. THE SO SHOULD HAVE ACTIVELY ASSISTED US IN DYNAMICALLY WORKING OUR APCH CHKLIST. I SHOULD HAVE NOTED THE OMEGA STILL DIRECTING MY DISPLAYS. SPLITTING THE NAV WITH THE R SIDE VERIFYING WITH RAW DATA WHAT THE L SIDE DOES. PROCESSED DATA SHOULD HAVE WORKED. THIS TIME IT DID NOT. WE FOLLOWED A STRATEGY OF 'ELEGANT DEGRADATION;' EVENTUALLY RELYING ON CTLR INSTRUCTIONS AND VISUAL APCH.