A C421 PVT PLT FLIES PAST HIS ORIGINAL ARPT WHILE ATTEMPTING AN ILS APCH AT JVY; EXPERIENCING AN UNAUTH RTE AND ALTDEVS.

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I WAS CLRED FOR THE ILS RWY 18 APCH INTO CLARK COUNTY ARPT (JVY). LOUISVILLE APCH GAVE ME VECTORS TO THE LOC AND SWITCHED ME TO COMMON TA FREQ. I HAD THE LOC FREQ IN NAV #1 AND A VOR FREQ IN NAV #2. THE AUTOPLT WAS ENGAGED; I NOTICED THAT IT WAS NOT ABLE TO KEEP THE LOC CAPTURED. I DECIDED TO CONTINUE THE APCH USING THE SECOND RADIO. I HAD TO REACH OVER TO THE NAV #2 (POSITIONED IN THE LOWER R CTR OF THE PANEL) TO DIAL IN THE LOC FREQ. THERE WAS A SUBSTANTIAL AMOUNT OF TURB AND GETTING THE RIGHT FREQ TOOK SOME TIME. WHEN I LOOKED BACK AT THE INSTS; I NOTICED THAT BOTH AIRSPD INDICATORS WERE AT ZERO. I IMMEDIATELY CHKED VERT SPD AND BANK. THE ACFT WAS IN A SLIGHT BANK. I FOUND THAT THE PITOT HEAT HAD BEEN JARRED INTO THE OFF POS. I RESET THE PITOT HEAT TO ON AND TRIED TO RECAPTURE THE LOC AND GS BY HAND FLYING OFF OF THE #2 RADIO AND USING THE CO-PLT HDG INDICATOR. I NOTICED THAT THE GS FLAG HAD DROPPED AND THAT I HAD OVERSHOT THE ARPT. I LOOKED OUT TO SEE LOUISVILLE SDF IN FRONT OF ME. I IMMEDIATELY MADE A CLBING L TURN AND CONTACTED APCH. THEY STATED THAT THEY HAD BEEN TRYING TO CONTACT ME AND THAT I HAD CAUSED OPERATIONAL PROBS (ACFT WERE DEVIATED AND DEPS DELAYED) AT THE LOUISVILLE ARPT. ANOTHER ACFT ATTEMPTED THE APCH AFTER MY ATTEMPT AND HAD TO GO MISSED. BECAUSE OF THIS AND THE FACT THAT I WASN'T SURE WHAT CAUSED THE PROB; I ELECTED TO LAND AT SDF FOR FUEL. THIS ARPT HAS MUCH LONGER/WIDER RWYS WITH BETTER APCH LIGHTING. I AGAIN USED THE AUTOPLT ON NAV #1; BUT WATCHED MY PROGRESS MUCH CLOSER. IT WAS NOT ABLE TO KEEP THE NEEDLE CAPTURED. I HAND FLEW THE REMAINING APCH TO THE ILS RWY 35 USING THE NAV #2 RADIO. I LANDED WITHOUT INCIDENT. I CONTACTED THE DEP SUPVR AS REQUESTED WHEN I LANDED. HE STATED THAT A 'PLTDEV' RPT WAS BEING FILED. I TOLD HIM THAT I BELIEVED THAT THE #1 NAV HAD MALFUNCTIONED. HOWEVER; ON CLBOUT FROM SDF IN IMC; THE HSI AND THE ATTITUDE INDICATORS DID NOT AGREE. THE HSI SHOWING A TURN ONE WAY AND THE ATTITUDE INDICATOR SHOWING A TURN THE OTHER WAY. APCH HAD TO CALL OUT MY HDG AND TELL ME WHEN I WAS FLYING LEVEL. I WENT TO ALTERNATE AIR AND RECYCLED THE BREAKER ON THE HSI. THE INSTS THEN AGREED AND I WAS ABLE TO COMPLETE THE FLT. I NOW BELIEVE THAT THE HSI WAS PROVIDING ERRONEOUS DATA TO THE AUTOPLT. THE REMAINDER OF THE FLT WAS FLOWN BY HAND AND USING THE CO-PLT'S HDG INDICATOR FOR REF. THE ACFT WILL NOT BE USED IN IMC CONDITIONS UNTIL THE PROBS ARE RESOLVED.