CRJ200 FLT CREW RECEIVES ACFT WITH WRITE-UP FOR ANTI-ICE DUCT FAULT. AFTER 5 HOUR DELAY FOR REPAIR FLT CREW DEPARTS TO DISCOVER REPAIR ATTEMPT HAS BEEN UNSUCCESSFUL ALONG WITH AN FMC DISAGREE MESSAGE THAT RESULTS IN A TRACK DEV. FLT CREW DIVERTS FOR REPAIRS.

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THE ACFT ARRIVED AT XA00. UPON TALKING TO THE ARRIVING CREW; THEY INFORMED ME THAT UPON DSCNT THEY RECEIVED AN 'ANTI-ICE DUCT' WARNING MESSAGE WHICH HE SUBSEQUENTLY ENTERED A MAINT WRITE-UP. THE ARRIVING CREW DEPARTED THE ACFT WHICH WE THEN ACCEPTED AND WAITED FOR MAINT TO ARRIVE. SOME TIME LATER MAINT ARRIVED AND INSPECTED THE WRITE-UP. THE MECH WORKED IN AND AROUND THE OUTSIDE OF THE ACFT FOR A PERIOD OF TIME AND SUBSEQUENTLY RETURNED TO THE COCKPIT TO INFORM ME THAT WE WOULD NEED TO RUN THE ACFT WITH BOTH ENGS TO SEE IF HE HAD REMEDIED THE PROB. WE PROCEEDED TO COORDINATE WITH BOTH OPS AND GND CTL TO PROCEED TO THE DEICE RUN-UP PAD. THE CREW WITH THE MECH ON BOARD PROCEEDED TO THE RUN-UP AREA WHERE WE RAN BOTH ENGS AND CHKED THE ANTI-ICE SYS UNDER THE DIRECTION OF THE MECH. WE RAN THE ENGS AND SYS FOR APPROX 8 MINS AT WHICH TIME THE MECH WAS SATISFIED THAT THE PROB HAD BEEN REMEDIED. WE RETURNED TO THE GATE WHERE THE MECH CLRED THE WRITE-UP AND FINISHED THE PAPERWORK AS WE PREPARED FOR DEP. THIS ENTIRE PROC TOOK APPROX 3 1/2 HRS FROM THE ARR OF THE ACFT THAT WAS ALREADY LATE. AFTER THE PAPERWORK WAS COMPLETED THE MECH LEFT THE AREA AND PAX WERE ENPLANED FOR THE DEP. WE PREPARED THE ACFT FOR DEP COMPLETING CHKLISTS AND PAPERWORK DURING THIS TIME. SHORTLY AFTER THE APU WAS STARTED AND THE BLEEDS SWITCHED ON; WE RECEIVED THE 'APU LCV FAIL' CAUTION MESSAGE. WE ONCE AGAIN CALLED MAINT THAT SUMMONED THE MECH TO RESOLVE THE APU WRITE-UP. ONCE AGAIN; THE MECH ARRIVED (APPROX 45 MINS LATER) AND DEFERRED THE APU. DURING THE DEFERRAL PROCESS THE MECH SWITCHED PWR SOURCES SEVERAL TIMES FROM GND PWR TO APU AND SO FORTH; FINALLY WE WERE READY FOR DEP. WE BECAME AIRBORNE AT APPROX XE15 LCL. AT APPROX 17000 FT WE ENCOUNTERED ICING CONDITIONS; WE TURNED ON THE WING ANTI-ICING SYS (COWLS WERE ALREADY ON). AT THIS TIME THE FMS PRESENTED AN 'FMS POS' MESSAGE; I ATTEMPTED TO VERIFY THE ACFT POS AND INITIALIZE THE FMS WHEN APPROX 5-7 MINS AFTER THE FMS MESSAGE APPEARED; WE RECEIVED THE 'ANTI-ICE DUCT' MESSAGE AND MASTER WARNING. I ABANDONED THE FMS RE-INITIALIZATION PROCESS TO DEAL WITH THE QRH PROCS. DURING THIS TIME; ATC HAD ISSUED 'DIRECT TO ABC' XMISSION. WE THEN ATTEMPTED TO NAV TO THE ABC FIX AND WERE SUBSEQUENTLY INFORMED BY ATC THAT WERE OFF COURSE BY APPROX 10 MI. AFTER THE COMPLETION OF THE QRH I CONTACTED MAINT VIA RADIO AND ADVISED THEM OF THE SITUATION. ONCE THE SITUATION WAS WELL IN HAND I THEN FOCUSED ON THE FMS PROB AND ACCOMPLISHED AN FMS RE-INITIALIZATION; WHICH WAS SUCCESSFUL. WE CONFERENCED IN WITH DISPATCH AND MAINT CTL REGARDING THE SITUATION AND DISCUSSED OPTIONS AND ALTERNATIVES. DUE TO AN INABILITY OF ACFT TO FLY IN ICING CONDITIONS; AND WITH FUEL RAPIDLY BECOMING AN ISSUE; DISPATCH AND I DECIDED THE BEST COURSE OF ACTION WAS TO DIVERT TO ZZZ WHERE THE CONDITIONS WOULD SUPPORT THE REQUIREMENTS NECESSARY. I SUBSEQUENTLY INFORMED THE CREW AND THEN MADE AN ANNOUNCEMENT TO THE PAX REGARDING THE DECISION TO DIVERT TO ZZZ. WE REQUESTED ROUTING FROM ATC AND SUBSEQUENTLY LANDED IN ZZZ. ALL CHKLISTS WERE PERFORMED PRIOR TO DEP AND ONCE AGAIN AFTER MAINT HAD COMPLETED THE INSPECTIONS AND DEFERRALS. I DO BELIEVE HOWEVER; THAT THE SWITCHING OF PWR SOURCES REPEATEDLY MAY HAVE CAUSED SOME TYPE OF MAP SHIFT OR INTERFERENCE WITHIN THE FMS. WE DID TOGA AND CONFIRMED RWY HDG AND FMS RWY SELECTION UPON DEP. DURING THE INITIAL ATTEMPT TO CORRECT THE FMS VIA NAVAID USE (NON-GPS EQUIPPED); MULTIPLE ATTEMPTS FOR THE FMS TO RECOGNIZE VOR SIGNALS FAILED. IT WAS DURING THIS PROCESS THAT THE WARNING MESSAGE PRESENTED.