ATP GA PLT TELLS OF PLT DISTR TASK WHILE EXPERIENCING ACFT EQUIP PROBS MALFUNCTIONS BEFORE AND AFTER BECOMING SINGLE PLT IFR. DIVERSION TO ALTERNATE ARPT.

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FLT BEGAN WITH VISIBILITY OVER 6 MI AND BEGAN TO DETERIORATE AS FLT PROGRESSED. GND FOG WAS FORMING. CEILINGS WERE INITIALLY OVER 3000 MSL THEN WENT DOWN AS I APCHED THE MOUNTAINS. I HAD A REMOTE COMPASS GYRO COMPUTER FAILURE WHICH FAILED THE HSI/HDG AND AUTOPLT. AT THAT TIME I CALLED ATC; RPTED THE FAILURE; AND REQUESTED AN IFR DUE TO THE LOWERING CONDITIONS. I RECEIVED A DISCRETE CODE AND CLRNC TO CLB TO 4000 AND DO THE APCH TO N13. INITIALLY I HAD A DIFFICULT TIME HOLDING TRACK DUE TO DISTR OF FINDING OUT WHAT WAS WORKING AND WHAT WASN'T AND WHY. (THERE WAS NO FLAG.) I DID THE APCH AND MISSED DUE TO THE LOW CEILINGS. I DID SEE GND AT ONE POINT AND TRIED BRIEFLY TO DSND THROUGH THE HOLE BUT ENTERED THE CLOUDS AGAIN. AT THAT TIME I CLBED TO 4900 AND RPTED THE MISSED TO ATC. I SHOULD HAVE LEVELED OFF AT 4000 FT. I BELIEVE I SHOULD NOT HAVE BEEN SO DISTRACTED BY THE EQUIP FAILURE. I HAD THE TRAINING; AND CURRENCY TO FLY THE ACFT WELL WITHOUT THE GYRO SYS. THE DISTR WAS THE FACTOR IN DEGRADATION OF FLYING SKILL. REVERTING BACK TO BASICS AND NOT TRYING TO TROUBLESHOOT A FAILURE IN DETERIORATING WX WOULD BE A BETTER PLAN OF ACTION.