B737 FO REPORTS HSI MALFUNCTION ON DEPARTURE CAUSING HEADING DEVIATION. OTHER RELATED PROBLEMS CAUSE FLT CREW TO ELECT TO RETURN FOR MAINTENANCE.

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WE WERE CLRED BY TWR TO FLY HDG 015 DEGS AFTER TKOF. UPON BEING CLRED FOR TKOF; I RAN UP THE THROTTLES AND HIT TOGA FOR TKOF. THE COMMAND BARS CAME DOWN AND WENT BACK OUT OF VIEW. I HIT THE BUTTON 2 MORE TIMES WITH SIMILAR RESULTS. I THOUGHT I HAD DISENGAGED THE TOGA BY HITTING IT TWICE LIKE I HAD. I FINALLY JUST IGNORED THE DISTR AND CONTINUED WITH THE TKOF WITHOUT THE TOGA FUNCTION. AFTER TAKING OFF AND PASSING 400 FT; I BEGAN A VERY SHALLOW TURN FOR THE 15 DEG ASSIGNED HDG. WE WERE COMING UP TO THE 1000 FT CALL TO RAISE FLAPS TO 1 DEG WHEN I NOTICED THE HDG FLAG ON MY HSI AND THE COMPASS ROSE NOT MOVING. I XREFED WITH THE PLT SIDE AND REALIZED THAT I HAD OVERSHOT THE HDG ASSIGNED BY ABOUT 15 DEGS. I IMMEDIATELY TURNED TO CORRECT THE HDG AND TOLD THE CAPT I HAD A PROB WITH THE DISPLAY ON MY SIDE. THE CAPT STARTED THE APU IN CASE THERE WERE ELECTRICAL PROBS AND WE XFERRED ACFT CTL SINCE HIS SIDE SEEMED TO BE WORKING CORRECTLY. WE WERE GIVEN THE DEP CTL SWITCH BY TWR AND QUESTIONED WHY WE HAD DEVIATED ON OUR HDG ASSIGNMENT. WE BRIEFLY TOLD THE TWR THAT WE HAD A DISPLAY MALFUNCTION BUT DIDN'T ELABORATE ON THE SITUATION. AFTER CHKING IN WITH DEP; WE CONTINUED TO TROUBLESHOOT THE PROB. PUTTING THE APU GENERATOR ON LINE DIDN'T HELP; BUT USING THE COMPASS/IRS XFER SWITCH CORRECTED THE PROB. WE SWITCHED ACFT CTL AGAIN AND WERE CONTINUING THE FLT SINCE THINGS SEEMED TO BE OPERATING NORMALLY ON THE ASSIGNED HDG BY DEP CTL. WE CHKED CIRCUIT BREAKERS AND GOT IN THE QRH FOR ANY FURTHER GUIDANCE. UPON FURTHER DISCUSSION; WE DECIDED THAT OUR NEXT CITY WOULD NOT HAVE ANY MAINT AND THAT WE WOULD GND THE PLANE AND MAKE THINGS WORSE DOWN-LINE IF WE CONTINUED. WE DECIDED TO RETURN TO ZZZ TO REPAIR THE PROB. WHEN I TRIED TO USE THE LNAV TO GO TO THE ASSIGNED POINTS FROM ATC; I DISCOVERED THAT IT WAS GIVING FURTHER ERRONEOUS INFO. I GAVE CTL OF THE ACFT TO THE CAPT AND WE CONTINUED WITH THAT FOR THE REST OF THE FLT. THE REST OF THE FLT WAS UNEVENTFUL. MAINT REPLACED THE ADC #2 AND REALIGNED THE IRS TO CORRECT THE PROB AFTER WE TAXIED BACK TO THE GATE. I BELIEVE THAT THIS WOULD BE VERY DIFFICULT TO CORRECT. THINGS HAPPENED SO FAST WITH SO MUCH GOING ON IN THAT CRITICAL PHASE OF FLT. THE TURN WAS SO SHALLOW THAT IT WAS EASY TO OVERSHOOT; BELIEVING THAT I STILL HAD FURTHER TURN TO GO. MY CONCENTRATION ON THE TKOF IS ON THE ADI; NOT THE HSI. BY THE TIME I NOTICED THE WARNING FLAG FOR HDG; WE WERE ALREADY LIKELY DRIFTING THROUGH THE ASSIGNED HDG. I THINK THE ONLY THING THAT WOULD HAVE HELPED WOULD BE A QUICKER XCHK BY MYSELF OR THE CAPT. I THINK THE TWR SHOULD HAVE ASKED US TO CHK OUR HDG. HE PROBABLY WOULD HAVE IF THERE WERE ANY OTHER ACFT BEING AFFECTED OR IF WE HADN'T CORRECTED SO QUICKLY. I THINK THIS COULD EASILY HAPPEN AGAIN IF THE CIRCUMSTANCES WERE REPEATED. I FEEL LIKE THIS WAS A 'PERFECT STORM' SERIES OF EVENTS LEADING UP TO THE SITUATION. SMARTER PEOPLE THAN ME WILL HAVE TO COME UP WITH A BETTER SOLUTION TO PREVENT THIS FROM EVER HAPPENING AGAIN.