HDG TRACK DEV CREATES A POTENTIAL CONFLICT WITH OTHER ACFT. IAP ILS APCH.

Narrative

HAD TUNED AND IDENTED LGA RWY 04 ILS. APCH CTL VECTORED US ON 070 DEG HDG TO INTERCEPT ILS LOC AND PROCEED INBOUND TO RWY 04 AT LGA. LOC CDI DID NOT APPEAR ON HSI OR ADI -- OVERSHOT LOC; GOT TA ON TCASII; TURNED TO 350 DEG HDG TO RE-INTERCEPT; GOT CLRNC TO DSND TO 3000 FT FROM APCH; THEN GOT RA ON TCASII WITH STEEP CLB COMMAND. WE COMPLIED. TFC PASSED 4 OR 5 MI TO OUR R THROUGH OUR ALT. TCASII STATED 'CONFLICT RESOLVED' (OR WHATEVER THE WORDING IS). WE RPTED TO LGA TWR THAT ILS WAS APPARENTLY NOT WORKING PROPERLY. THEN; I REALIZED THE APCH COURSE WE HAD IN ILS RECEIVER WAS 173 DEGS INSTEAD OF THE REQUIRED 044 DEGS. I SET ILS COURSE TO 044 DEGS. ILS INDICATIONS BECAME NORMAL. LGA TWR ASKED IF ILS WAS OPERATING NORMALLY. WE REPLIED THAT IT WAS. CAUSE OF ALL THIS WAS ILS COURSE SET INCORRECTLY. I KNEW IT MADE A DIFFERENCE; BUT FO AND JUMPSEAT CAPT BOTH WERE SURPRISED. ALL OTHER ACFT WE HAD FLOWN (LGT; MLG; WDB); THE INCORRECT COURSE WOULD NOT AFFECT INTERCEPT; BUT LGT/WDB (2 ENG) DEFINITELY DOES REQUIRE EXACTLY CORRECT COURSE.