CRJ200 FLT CREW HAS A HDG AND TRACK DEV DEPARTING LGA.

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WHILE ON THE GND AT LGA TAXIING INTO POS AT RWY 13; WE RECEIVED AN EFIS COMPASS MONITOR MESSAGE. WE BOTH WENT INTO DIRECTIONAL GYRO MODE AND SET THE COURSE TO RWY HDG. AFTER DEPARTING RWY 13 AND FLYING A 180 DEG HDG; WE WENT BACK TO MAGNETIC MODE. WE ONCE AGAIN RECEIVED AN EFIS COMPASS MONITOR MESSAGE. AS I CHKED WITH DEP I WAS GIVEN A SQUAWK CODE TO ENTER AS I WAS DISTR WITH THE SQUAWK AND EFIS COMPASS MONITOR MESSAGE. AFTER ENTERING THE SQUAWK CODE WE WERE ASKED OUR HDG. AS I READ OUR HDG; I REALIZED THAT WE WERE OFF COURSE AND THAT THE CAPT'S AND MY DIRECTIONAL GYRO WERE WAY OFF COURSE. WE WERE GIVEN A HDG TO FLY. AS WE WERE WHAT APPEARED TO BE ON THE NEW HDG; WE WERE ACTUALLY STILL 30 OR MORE DEGS OFF COURSE; DEPENDING ON WHICH DIRECTIONAL GYRO YOU WERE LOOKING AT. AS WE WERE TRYING TO SET THE HDG FROM THE COMPASS WE ALSO REALIZED THAT THE COMPASS APPEARED TO BE HANGING. ENRTE THE COMPASS WAS OBSERVED AS FREE AND CLR. THIS ONLY CONFUSED THE SITUATION GREATER. AFTER RECEIVING NUMEROUS HDG READOUTS FROM DEP; WE WERE ABLE TO GET THE DIRECTIONAL GYROS REALIGNED. THIS PROCESS TOOK ABOUT 15 MINS UNTIL WE COULD REMEDY THE PROB. I BELIEVE THE MAJOR CAUSE OF THE PROB IS ALL THE METAL ASSOCIATED WITH RWY 13 AT LGA. ANOTHER FACTOR WAS THE DISTRS OF THE MULTIPLE RADIO CALLS; CLEANING UP THE ACFT AND PERFORMING THE CLB CHKS. A POSSIBLE REMEDY TO HELP SOLVE THIS REOCCURRENCE IS ELEVATED CROSS-EXAM OF HDG WHILE DEPARTING RWY 13 LGA. ALSO WAIT A LONGER PERIOD TO SWITCH FROM DIRECTIONAL GYROSCOPE TO MAGNETIC MODE. UPON LNDG IN RDU; WE WERE NOTIFIED BY THE FLT ATTENDANT THAT A PAX HAD BEEN ASKED NUMEROUS TIMES TO TURN OFF PDA WITH BLACKBERRY. FLT ATTENDANT WAS CONVINCED THAT THE PAX HAD IN FACT TURNED IT OFF BEFORE TKOF. IN FACT; THE PAX HAD NOT TURNED IT OFF UNTIL WELL AFTER TKOF AND IT WAS STILL BEING OPERATED. THIS WAS DISCOVERED BY THE CAPT AFTER TALKING TO THE PAX IN RDU.