B737-300 CREW LANDED AT LAX WITHOUT CLRNC IN WX BELOW CAT I MINIMUMS.

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WE WERE MAKING A CAT IIIA APCH TO RWY 24R AT LAX. THE CEILING WAS 200 FT INDEFINITE AND THE VISIBILITY HAD BEEN AS LOW AS 1/4 MI. SOCAL APCH HAD CLRED US FOR THE ILS 24R AND TOLD US TO CONTACT THE TWR AT ROMEN. AS WE EXTENDED THE FLAPS THE 'LE FLAP TRANSIT' LIGHT ILLUMINATED AND REMAINED ON. SINCE THE CAPT WAS FLYING I PULLED OUT THE QRH AND BEGAN TO WORK THE CHECKLIST. WHILE WE WERE GOING THROUGH THE CHECKLIST SOCAL ASKED US TO DO A RIGHT 360 DEG TURN IN ORDER TO ALLOW A LIFEGUARD FLT TO MOVE IN FRONT OF US. ABOUT HALF WAY THROUGH THE TURN WE WERE AGAIN CLRED FOR THE APCH AND GIVEN A DSCNT TO A LOWER ALT TO INTERCEPT THE LOC. I WAS WORKING QUICKLY TRYING TO COMPLETE THE CHECKLIST AND ALSO KEEP AN EYE ON OUR FLT PATH. WE WERE ABLE TO CLR THE FLAP PROB AND REESTABLISH OURSELVES ON THE APCH JUST OUTSIDE ROMEN. AT THIS POINT I THOUGHT I HAD SWITCHED OVER TO LAX TWR; BUT THERE WAS A LOT OF CONVERSATION ON THE FREQ SO I WAITED TO CHECK IN. WE WERE APCHING 1000 FT SO I LOOKED OVER AT HGS CTL PANEL TO CHECK THAT THE CAT IIIA MODE WAS ACTIVE. HOWEVER; DUE TO GLARE; I COULD NOT SEE THE DISPLAY CLRLY SO I REACHED OVER TO ADJUST THE BRIGHTNESS. I THINK THAT AS I REACHED TO ADJUST THE BRIGHTNESS ON THE HGS PANEL THAT I MAY HAVE INADVERTENTLY FLIPPED THE TOGGLE SWITCH ON THE #1 COM RADIO BACK TO THE SOCAL APCH FREQ WITHOUT REALIZING IT. THE CAPT MADE HIS 1000 FT CALL OUT WHICH I REPEATED BACK TO HIM AND INCLUDED 'MODE IIIA.' I TURNED MY ATTENTION TO THE FLT INSTRUMENTS; FOLLOWED OUR FLT PATH; MADE MY CALL OUTS; AND REHEARSED IN MY MIND WHAT I WOULD NEED TO DO IN THE EVENT OF A MISSED APCH. WE LANDED ON 24R AND PULLED OFF ON THE REVERSE HIGHSPEED. AFTER A FEW MOMENTS I NOTICED THAT WE WERE ON THE WRONG RADIO FREQ. I SWITCHED TO THE TWR FREQ AND WE WERE CLRED TO CROSS 24L. UPON REACHING THE GATE WE CONTACTED THE LAX TWR SUPVR. HE WANTED TO BE SURE THAT WE UNDERSTOOD THAT THE PROCEDURE AT LAX WAS TO REMAIN ON TWR FREQ UNTIL WE WERE CLR OF BOTH RWYS. WE EXPLAINED WHAT HAD HAPPENED AND HE WAS SATISFIED AND SAID THAT NOTHING FURTHER WOULD BE DONE. IN RETROSPECT; I RECOGNIZE NOW THAT AS MY WORKLOAD INCREASED THAT MY SITUATIONAL AWARENESS DECREASED. THIS KIND OF 'TUNNEL VISION' OR FIXATION IS COMMON IN BUSY/STRESSFUL SITS. I THOUGHT THAT I HAD EVERYTHING UNDER CTL. I DID NOT REALIZE THIS WAS HAPPENING TO ME. HOWEVER; I MISSED A VERY IMPORTANT ELEMENT; I DID NOT CONTACT THE TWR UNTIL AFTER WE LANDED. THE LESSON I LEARNED IS TO SLOW DOWN; ASK TO BE RESEQUENCED; OR TAKE A DELAY VECTOR. DON'T HURRY THROUGH YOUR PROCEDURES OR YOU WILL PROBABLY MAKE A MISTAKE.