B737-800 FLT CREW MAKE WRONG RWY APCH AT DFW.

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DURING DSCNT INTO DFW FROM THE W AT APPROX XA00 AM ON A WET AND DARK MORNING AT ABOUT 3000 FT; WE WERE BEING VECTORED TO A DOGLEG AND ASKED IF RWY 35C WAS IN SIGHT. WE REPLIED THE ARPT WAS IN SIGHT; NOT THE RWY. DFW APCH CTL THEN CLRED US FOR A VISUAL APCH TO RWY 35C. ALL NAVAIDS WERE SET FOR THE ILS TO RWY 35C; HOWEVER; THE CAPT WAS STILL IN THE OTHER PROCESS OF ATTEMPTING TO RECEIVE A VALID IDENT ON THE LOC FREQ. BOTH OF US HAD MAP MODE SELECTED ON OUR NAV DISPLAYS. LOOKING AT THE ARPT FROM OUR VANTAGE POINT; THERE WAS ONLY ONE SET OF APCH LIGHTS VISIBLE (MALSR). I THEN ARMED THE APCH MODE OF THE AUTOPLT AND WAITED FOR THE INTERCEPT. THE CAPT STATED HE DID NOT YET HAVE A VALID LOC IDENT AND AT ABOUT THE SAME TIME; IT APPEARED WE WOULD OVER SHOOT THE FINAL APCH COURSE ASSOCIATED WITH THE BRIGHT APCH LIGHTS. I TURNED THE ACFT TO LINE UP ON FINAL AND THEN CHKED BOTH NAV DISPLAYS. I NOTICED THAT BOTH OF OUR DISPLAYS WERE NOT ALIGNED WITH THE SELECTED RWY AND FOR A BRIEF MOMENT; THOUGHT IT COULD BE A MAP SHIFT. I SWITCHED TO RAW DATA ON MY NAV DISPLAY; AND IT CONFIRMED WE WERE LEFT OF COURSE. THE CAPT MEANTIME HAD BEEN OCCUPIED RUNNING CHKLISTS; SETTING AIRSPD BUGS; AND ATTEMPTING TO OBTAIN AN IDENT ON THE LOC FREQ. I NOTIFIED HIM OF THE DISCREPANCY AND BY THIS TIME; WE WERE APCHING; OR AT; 1000 FT AGL. WE BOTH ACKNOWLEDGED THE DISCREPANCY AND WERE ALSO UNABLE TO DETERMINE IF THE LOCATION OF THE MAIN TERMINAL WAS TO THE L OR TO THE R OF THE RWY WE WERE ALIGNED WITH. (THIS WOULD HAVE GIVEN US EVEN FURTHER CLUES OF OUR ERROR). JUST AS WE CONCLUDED THE APCH SHOULD NOT BE CONTINUED; TWR CALLED AND ASKED IF WE WERE AWARE THAT WE WERE ALIGNED WITH RWY 36R. THE CAPT ACKNOWLEDGED; HOWEVER; TWR SAID THERE WERE NO CONFLICTS; AND WE WERE CLRED TO CONTINUE TO RWY 36R AND LAND. IN RETROSPECT; I SHOULD NOT HAVE SOLELY FOCUSED ON THE FIRST AND ONLY SET OF APCH LIGHTS I SAW. ALSO; KEEP IN MIND THE CORRECT APCH LIGHTS YOU SHOULD BE OBSERVING. TRUST YOUR RAW DATA INSTS. GET THE OTHER PLT 'IN THE LOOP' AS SOON AS POSSIBLE IF SOMETHING LOOKS OR FEELS ABNORMAL.