ACR MLG ACFT FMC PROBLEM RESULTED IN THE ACFT DEVIATING FROM ASSIGNED TRACK.

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DURING TKOF FROM PIT AT A SPD OF APPROX V1; A MESSAGE APPEARED IN THE SCRATCH PAD WHICH READ; VERIFY PRESENT POS. THIS OCCURRED RIGHT AT LIFTOFF AND I THOUGHT DID NOT INCLUDE A RETURN TO PIT. THE DEP WAS A VECTOR SID AND NO NEED FOR VOR NAV. I COULD TELL FROM OUR FIX PAGE WITH REF TO THE FMI; DME; RADIAL COMPARISON THAT THE MAP MODE WAS NOT CORRECT. IT APPEARED TO ME THAT WE HAD A MAP SHIFT. MY FO WAS NEW. SECOND LINE FLT SINCE IOE. I INSTRUCTED HIM TO REVIEW THE ENRTE CHARTS FOR VOR CROSS RADIALS SO AS TO GET A FIX ON OUR PRESENT POS. IT WAS A SHORT FLT ONLY 1 HR IN LENGTH AND PIT DEP AS WELL AS CLEVELAND CTR HANDLED US WITH RADAR VECTORS. WE WERE UNABLE TO FLY DIRECTLY OVER A NAV FIX SUCH AS A VOR. THE INFO IN MAP MODE WAS IN ERROR BY SOME 5 MI AS BEST I COULD DETERMINE. ANOTHER PROBLEM I HAD WAS DETERMINING IF HDG INFO WAS ACCURATE. AT THE ALT OF 35000 FT WE WERE EXPERIENCING A XWIND OF 105 KTS. BECAUSE THE TFC WAS HVY WE WERE VECTORED L THEN R WITH SEVERAL LEVEL OFFS. WITH ALL THIS MANEUVERING; TRYING TO USE THE STANDBY COMPASS WAS NEXT TO IMPOSSIBLE. I WAS QUESTIONING IN MY OWN MIND IF HDG INFO WAS ACCURATE BECAUSE WITH A XRADIAL AS WELL AS HDG DIRECTLY TO A VOR THE WIND CORRECTION ANGLE WAS VERY LARGE BECAUSE OF THE WIND. THIS APPEARED TO BE INACCURATE THOUGH IT MAY NOT HAVE BEEN. I HAD THE COPLT FLY EVEN THOUGH THE AUTOPLT WAS ENGAGED SO I COULD THINK AS WELL AS BETTER MANAGE THE COCKPIT. WHEN WE WERE TURNED OVER TO CHICAGO APCH; WE WERE GIVEN A HDG TO INTERCEPT THE 130 DEG RADIAL OF ORD. THE RECIPROCAL AND INBOUND COURSE IS 310 DEGS; HOWEVER MY COPLT SAID 330 DEGS. THE COCKPIT WORKLOAD WAS HIGH AND I DIDN'T QUESTION IT. A SHORT TIME LATER; CHICAGO APCH CALLED AND ASKED IF WE WERE TURNING TO INTERCEPT? REALIZING THE ERROR; I TUNED IN COURSE OF 310 DEGS BUT BY THEN APCH REQUESTED A TURN TO 350 DEGS. I THEN INFORMED APCH CTL OF OUR PROBLEM AND STATED A MAP SHIFT AND RNAV INOP. WE WERE VECTORED TO FINAL FOR 14R ILS AND LANDED WITHOUT FURTHER INCIDENTS.