CRJ FLT CREW DEPARTING DFW RWY 35L EXPERIENCES COMPASS MALFUNCTION CAUSING LOSS OF SEPARATION WITH MD80 DEPARTING RWY 36R.

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CLASSIC CHAIN OF EVENTS: DEFERRED EQUIP; LAST MIN CHANGES IN CLRNC; EXPERIENCE LEVEL. DALLAS 8 DEP WITH DEFERRED FMS AND TCAS. JUST AFTER TKOF 'EFIS COMP MONITOR' CAUTION MESSAGE. AS PNF; I ATTEMPTED TO CORRECT THE PROB AND DETERMINE WHICH DIRECTIONAL GYRO WAS ACCURATE. TWR ASSIGNED A 030 DEG HDG. AFTER ALIGNING THE HDGS ON THE DIRECTIONAL GYRO THE PROB OCCURRED 3 MORE TIMES WHILE CLBING TO 10000 FT. WE WERE UNABLE TO DETERMINE AN ACCURATE HDG DURING CLBOUT WITH THE STANDBY COMPASS. ATC ASKED ME TO CALL. USED FMS ENRTE NAV. FIX EQUIP INSTEAD OF DEFERRING IT. SUPPLEMENTAL INFO FROM ACN 738773: IMMEDIATELY ON LIFT-OFF WE HAD CAUTION LIGHTS AND MESSAGE FOR 'EFIS COMP MON;' THE AFFECTED DIRECTIONAL GYRO TURNED OUT TO BE ON MY SIDE (PF). I THEREFORE CONTINUED TO HAND FLY THE ACFT USING A COMBINATION OF STANDBY COMPASS AND THE CAPT'S INDICATION WHILE HE TRIED TO RECTIFY MY DIRECTIONAL GYRO INDICATION BY SLEWING IT. THE DEP HAD NO DEPICTION OF THE ROUTING ON THE PFD; AND NO COURSE TO TAKE INTO ACCOUNT WIND DRIFT; SINCE IT ONLY CONSISTED OF A HDG. SEVERAL 'EFIS COMP MON' CAUTION MESSAGES AND ERRORS CONTINUED TO OCCUR. I DO BELIEVE WE ACCURATELY CONTINUED TO FLY THE PUBLISHED HDG; DESPITE THE INDICATION ERRORS. TWR GAVE US A FREQ CHANGE; AT THAT MOMENT THE 'EFIS COMP MON' CAUTION RETURNED (WITH FLASHING LIGHTS) AND THE CAPT ATTEMPTED TO FIX AGAIN. THIS CAUSED A MOMENTARY DELAY IN SWITCHING FREQS. I QUERIED THE CAPT IF HE HAD CHKED IN ON THE NEW FREQ; BUT THEN THE TWR CTLR ASKED IF WE WERE STILL ON TWR FREQ; AND ASKED US TO FLY 030 DEGS FOR TFC AND CONTACT DEP. THE CAPT TOLD THE CTLR THAT WE HAD AN EQUIP ISSUE HE WAS RESOLVING. WE IMMEDIATELY FLEW 030 DEGS AS REQUESTED; AND THE CAPT CONTACTED DEP. NOTIFIED BY ATC TO COPY DOWN TELEPHONE NUMBER. ENTERED ENRTE PORTION OF FLT; WHERE WE WERE ABLE TO USE FMS/AUTOPLT. MAINT TESTED SYS ON ARR. QUICK RESOLUTION OF EQUIP ERRORS SO MAX NAV EQUIP AVAILABLE TO CREW. ATC NOT REQUIRE HDG CHANGES FOR TFC DURING INITIAL CLB. SUPPLEMENTAL INFO FROM ACN 739292: ON RNAV DEP; BLECO; RWY 36R. ON INITIAL CLBOUT NOTICED AN RJ ON DEP FROM RWY 35L. HE WAS SLIGHTLY IN FRONT; APPROX 1 O'CLOCK POS. HE APPEARED TO BE DRIFTING SLIGHTLY W; TOWARD OUR RTE OF FLT. I KEPT AN EYE ON HIM; HE DID NOT APPEAR TO BE A THREAT. SHORTLY AFTER; TWR TOLD US TO TURN 30 DEGS TO THE L. I ALSO NOTED THE RJ TURNING TO THE R. WE WERE THEN INSTRUCTED TO RESUME OUR OWN NAV. TWR STATED WE HAD DONE NOTHING WRONG AND THAT THEY WOULD HANDLE IT. I ASKED IF THEY NEEDED A RPT; THEY SAID NO. BECAUSE OF THE VFR CONDITIONS AND HAVING THE RJ IN SIGHT; I DO NOT BELIEVE IT WAS A NEAR MISS SITUATION OR I WOULD HAVE TAKEN EVASIVE ACTION. WE DID NOT GET A TA/RA AT ANY TIME. IF WE HAD BEEN IN THE WX AND THE TRACKS NOT BEEN ALTERED; THEN IT COULD HAVE DEVELOPED INTO A MORE SERIOUS SITUATION. I BELIEVE TWR DID A NICE JOB ENSURING SAFETY WOULD BE MAINTAINED.