B757-200 FLT CREW REPORTS GO AROUND AT SEQU AFTER FAILURE TO ACQUIRE LOC DURING ILS TO RWY 35.

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ARRIVING AT SEQU; APCH WAS CTLING OUR SPD. THERE WAS AN ACFT AHEAD OF US AND WE WERE IN THE CLOUDS. WE MADE THE TURN AT 16 DME AND DSNDED TO 12000 FT; BUT NOTICED THAT SOMETHING WAS WRONG. WE WERE W OF THE LOC (THE MAP DISPLAY SHOWED US W; WE GOT A GLIMPSE OF THE GND WHICH CONFIRMED IT; AND SEQU APCH SAID SOMETHING) WITH THE LOC NEEDLES IN THE COCKPIT INDICATING THAT WE WERE STILL E. THE LOC NEVER CAPTURED. WE HAD NOT ARMED THE GS YET. SOMETHING WAS NOT RIGHT; SO WE EXECUTED A MISSED APCH AND RETURNED FOR AN UNEVENTFUL LNDG. I AM STILL NOT SURE WHAT HAPPENED; BUT IT DIDN'T LOOK RIGHT. IT WAS VERY BUSY AND NOT AN EASY EVENT TO HANDLE WELL. THE CAPT HAS BEEN INTO SEQU HUNDREDS OF TIMES AND I HAVE BEEN THERE DOZENS OF TIMES (8 YRS FLYING THERE). WITH 2 EXPERIENCED SEQU PLTS WE HAD OUR HANDS FULL. HERE IS WHAT I HAVE SAID BEFORE AND WILL SAY AGAIN. WATCHING A VIDEO WILL NOT CUT IT FOR NEW GUYS INTO SEQU. IT IS UNSAFE TO SEND GUYS DOWN THERE WITH A VIDEO CHKOUT. SUPPLEMENTAL INFO FROM ACN 761604: UPON ARR TO SEQU (IFR CONDITIONS HVY PRECIP); ATC KEPT US CLOSE TO TFC; AS WE TRIED TO SLOW AS MUCH AS POSSIBLE. UPON LOC CAPTURE ATC TRIED TO VECTOR US OFF TO THE L. WE DECLINED DUE TO THE HIGH TERRAIN. ATC SAID OK CONTINUE APCH AND SLOW AS MUCH AS POSSIBLE. AS WE PICKED UP THE LOC IT WAS SWAYING BACK AND FORTH (MAYBE DUE TO THE ACFT BTWN US AND THE RWY). FMC DISPLAY DID NOT AGREE WITH LOC EITHER. WE ELECTED TO ABANDON THE APCH AND PERFORM A GAR. ON THE GAR WE WERE ASSIGNED 13000 FT FOR THE VECTORS (STILL IN IFR CONDITIONS). WE ASKED FOR 16000 FT DUE TO THE TERRAIN AND IT WAS APPROVED. CAME AROUND FOR ANOTHER APCH AND LANDED.