HDG TRACK DEV WHEN A DEP MD80 FLT CREW EXPERIENCES COMPASS AND HSI PROBS WITH BOTH COMPASSES AND OTHER ASSOCIATED EQUIP BECAUSE OF MAGNETIC INTERFERENCE NEAR RWY 13 AT LGA.

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LONG DELAYS AT LGA DUE TO WX. WE SPENT A LOT OF TIME HOLDING NEAR THE APCH END OF RWY 13. JUST PRIOR TO TAKING THE RWY; THE NO AUTOLAND LIGHT CAME ON DUE TO SLIGHT DIFFERENCES IN HDG. I MENTIONED THAT; AS PER THE 10-7 PAGES; THAT WASN'T UNUSUAL FOR OUR LOCATION ON THE ARPT. WE WERE GIVEN A REVISED CLRNC TO 3000 FT AND ASSIGNED THE WHITESTONE CLB. AT THE BEGINNING OF THE TKOF ROLL; WE GOT A HDG ANNUNCIATOR ON THE FMA AND I ELECTED TO CONTINUE THE DEP. SHORTLY AFTER LIFTOFF; THE FLT DIRECTOR DISAPPEARED. I TOLD THE FO TO TRY TO FLY THE DEP USING HIS HDG BUT ADDED TO THE CONFUSION BY NOT TELLING HIM WHICH COMPASS TO USE. OUR DEP HDGS WERE CLOSE; BUT NOT PRECISE; AND MAY NOT HAVE FOLLOWED THE NOISE ABATEMENT ROUTING. WE COMPLIED WITH ALL OTHER ALT AND SPD REQUIREMENTS. SHORTLY AFTER THE TURN TO 040 DEGS; I ADVISED ATC OF OUR HDG PROBS AND HE PROVIDED VECTORS AS NEEDED. I TRIED TO XCHK THE STANDBY COMPASS BUT; EVEN THOUGH THE LIGHT WAS OK; I WAS UNABLE TO SEE THE NUMBERS DUE TO AMBIENT LIGHT CONDITIONS IN THE COCKPIT. (IT ALWAYS WORKS IN THE DARK SIMULATOR BUT IS PRETTY WORTHLESS ON A BRIGHT AFTERNOON.) AFTER ABOUT 5 MINS; THE COMPASSES WERE BACK IN SYNC AND THE FLT PROCEEDED UNEVENTFULLY. THIS WAS THE LAST LEG OF THE DAY AND WE WERE BOTH GETTING TIRED AFTER THE LONG DELAYS. IF I HAD BEEN FRESH; I PROBABLY WOULD HAVE FIXED THE PROB BEFORE TKOF INSTEAD OF DECIDING THAT THE HDGS WERE GOOD ENOUGH FOR A VMC DAY. SUPPLEMENTAL INFO FROM ACN 618576: THE CAPT HAD ALREADY BRIEFED THE DEP NOTES CONCERNING MAGNETIC DEVS FOR RWY 13 DEPS. AFTER LIFTOFF; THE ROLL MODE BEGAN FLASHING HDG HOLD AND THE FLT DIRECTOR HDG MODE COULD NOT BE SELECTED. WE WERE BOTH CONCERNED BECAUSE THE NOISE ABATEMENT PROC REQUIRED AN IMMEDIATE R TURN TO A 180 DEG HDG FOLLOWED QUICKLY BY A L TURN TO A 040 DEG HDG. ADDITIONALLY; OUR INITIAL ALT WAS CHANGED FROM 5000 FT TO 3000 FT. I TURNED OFF MY FLT DIRECTOR AND FLEW RAW DATA. THE CAPT SAID USE YOUR SIDE FOR HDG INFO. I STARTED THE R TURN TO 180 DEGS AND ASKED WHICH ONE; MEANING HSI OR RMI. THERE WAS AT LEAST A 15 DEG DIFFERENCE IN THE HDGS. HDGS WERE BALLPARK AT BEST. WE RECEIVED SEVERAL VECTORS DURING THE DEP TO CLR TSTMS.