AN MLG HAD A HDG ERROR IN THE WX REQUIRING A GAR.

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DURING RADAR VECTORS FOR DSCNT AND APCH TO RWY 14R ORD; THE HDG LIGHT ON THE FMA ILLUMINATED. CAPT VERSUS FO'S HDGS INDICATED APPROX 10 DEGS DIFFERENCE. THE STANDBY COMPASS WAS 20-30 DEGS DIFFERENCE FROM #1 AND #2. THIS WAS THE FO'S LEG AND THE AUTOPLT WAS IN USE. #2 DFGC SELECTED. THE FO'S HSI COURSE BAR STUCK AT THE TOP OF THE CASE AND WE FLEW THROUGH THE LOC WHILE I WAS TROUBLESHOOTING THE HDG PROBLEM. ATC GAVE US A HDG TO REINTERCEPT THE LOC; BUT WE DID NOT HAVE RELIABLE HDG INFO AT THIS POINT; SO WE EXECUTED A MISSED APCH. WE WERE VECTORED W OF ORD IN AN EFFORT TO HEAD TOWARD AN ALTERNATE WHILE ANALYZING OUR MALFUNCTIONS. AFTER TALKING WITH ATC; DISPATCH; AND MAINT; I DECIDED WE COULD USE #1 DFGC AND #1 ILS AND ATTEMPT ANOTHER APCH AT ORD WITH SUFFICIENT FUEL TO FLY TO MSP (GOOD WX) IF UNABLE TO MAKE A SUCCESSFUL APCH AT ORD. WE LANDED UNEVENTFULLY ON THIS ATTEMPT. AFTER THE PAX DISEMBARKED; A FLT ATTENDANT TOLD ME THAT A MAN GOT OFF THE ACFT USING A CELLULAR TELEPHONE. SHE DID NOT KNOW IF HE WAS USING IT DURING THE TIME OF THE HDG MALFUNCTION. I DO NOT KNOW IF A CELLULAR TELEPHONE COULD MAKE HDGS DIVERGE LIKE THIS; BUT IF IT IS A POSSIBILITY; IT SHOULD BE EMPHASIZED DURING THE FLT ATTENDANT'S DEP PA. I AM SURE THAT HAD WE NOT HAD THE HDG PROBLEM THAT I WOULD HAVE HAD MY ILS TUNED IN SOONER AND CAUGHT THE LOC PROBLEM ON THE FO'S SIDE. I HAD MY VOR ON ORD TO KEEP TRACK OF WHERE WE WERE WHILE I CHKED THE HDGS. I ALSO USED A FLT ATTENDANT IN THE JUMPSEAT TO HELP MONITOR AND TALK TO DISPATCH WHILE WE WERE SO BUSY (THERE WERE NO PLTS DEADHEADING IN THE BACK). SHE REMAINED IN THE COCKPIT FOR LNDG BECAUSE SHE HAD COMPLETED HER DUTIES IN THE BACK AND I THOUGHT I MIGHT NEED HER TO TALK TO DISPATCH. (THEY WERE LOOKING FOR A CLOSER ALTERNATE.) CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTING CAPT STATES THAT THERE WERE 2 MALFUNCTIONS IN THIS INCIDENT. THE FO'S HSI STUCK TO THE SIDE OF THE CASE MECHANICALLY; PREVENTING THE COURSE BAR TO SWING WHEN IT SHOULD. THE CAPT'S NAV RADIO WAS TUNED TO ORD; NOT THE ILS; SO THERE WAS NO XCHK. THE COMPASS PROBLEM SEEMS TO HAVE BEEN FIXED BY CHANGING BOTH 'COMPASS RACK SLAVING AMPLIFIERS.' ELECTROMAGNETIC INTERFERENCE WAS RULED OUT BY COMPANY MAINT PERSONNEL; BUT THERE IS STILL SOME DOUBT IN THE CAPT'S MIND. THE COMPASSES DIVERGED WHILE IN A TURN AND CAME BACK VERY SLOWLY. THE STANDBY COMPASS IS VIEWED WITH THE USE OF 2 MIRRORS. AT 1 POINT; 1 HSI VARIED 20 DEGS AND THE OTHER VARIED 30 DEGS FROM THE STANDBY COMPASS. THIS CREW HAD FLOWN THE SAME ACFT 2 LEGS PREVIOUSLY THIS DAY WITH NO PROBLEM. ATC GAVE SUPERB HANDLING AND SEEMED TO BE PREPARED TO HANDLE THIS ACFT WITH NO REAL DIFFICULTY.