PRIMARY NAVIGATION AID STOPPED WORKING AND ACFT INADVERTENTLY PENETRATED THE CVG ARSA.

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I INADVERTENTLY VIOLATED THE GREATER CINCINNATI INTL ARPT ARSA. I ENTERED THE COORDINATES FOR LUNKEN FIELD; AND AFTER A FEW SECONDS; THE LORAN INDICATED THAT MY COURSE SHOULD BE 138 DEGS. WITH THE STRONG FOLLOWING NW WIND; MY HDG VARIED FROM 150-165 DEGS. GND SPD WAS STEADY AT 140-142 KTS. SE OF GARY THE SCATTERED CLOUD LAYER WAS HIGHER; SO I CLBED TO 7500' MSL; STAYING WELL CLR OF CLOUDS. THE AIR WAS SMOOTH. THE CLOUD LAYER CHANGED FROM SCATTERED TO BROKEN 75 NM'S NW OF LUNKEN; SO I DESCENDED THROUGH AND OPENING TO 3000' MSL. I ENCOUNTERED DECREASING VIS; MILD TO MODERATE TURBULENCE; ENE OF INDIANAPOLIS; AND I ALTERED MY COURSE WHEN NECESSARY TO AVOID LOW LEVEL CLOUDS. 50 NM'S NW OF LUNKEN; I ATTEMPTED W/O SUCCESS TO CONTACT LUNKEN TO CONFIRM VFR CONDITIONS. LUNKEN ATIS RPTED 3000' CEILINGS; GOOD VIS (10 MI; I BELIEVE). 40 NM'S NW OF LUNKEN I AGAIN ATTEMPTED W/O SUCCESS TO CONTACT LUNKEN TWR TO CONFIRM THEIR ATIS RPT. I AGAIN ATTEMPTED TO MAKE RADIO CONTACT AT 30 NM'S; AND SUCCEEDED AT ABOUT 28 NM'S. VFR WAS CONFIRMED. I WAS ENCOUNTERING GREATER TURBULENCE; MORE LOW LEVEL CLOUDS REQUIRING ALTERING COURSE FREQUENTLY. AT ABOUT 25 NM'S OUT; MY LORAN C STOPPED PROVIDING DISTANCE; DIRECTION; GS INFO. SINCE VISIBILITY WAS RPTED GOOD IN THE CINCINNATI AREA; I CHOSE TO CONTINUE MY COURSE BY DG; TAKING VOR FIXES OFF OF SHELBYVILLE AND CVG. 2 FIXES CONFIRMED MY POS NW OF LUK. ADF ALSO CONFIRMED A NW POS. FROM HAMILTON; HOWEVER; AS I GOT CLOSER TO CINCINNATI; I WAS ALARMED TO FIND MORE LOW LEVEL CLOUDS; INCREASING TURBULENCE AND THE CITY ITSELF WAS NOT VISIBLE. I ALTERED MY COURSE TO THE W SEVERAL TIMES TO AVOID LOW LEVEL CLOUDS. AT THIS TIME; W/O ANY OF THE LANDMARKS I HAD COUNTED ON VISIBLE; I BECAME FEARFUL THAT I MIGHT BE HEADING INTO THE CVG ARSA. I ATTEMPTED TO FIND THE CVG APCH FREQ ON MY WAC CHART; BUT FOUND THAT FLYING THE AIRPLANE AND REMAINING VIGILANT WAS ALL CONSUMING. MY WIFE WAS UNABLE TO HELP. WHEN I FINALLY SAW THE OHIO RIVER ORIENTED IN A NS DIRECTION; I KNEW THAT WE WERE EITHER W OF CVG OF S OF LUK. STILL; CINCINNATI WAS NOT VISIBLE THROUGH LOW CLOUD COVER. IT WAS AT THIS POINT THAT THE W END OF ACTIVE RWY 9L-27R BECAME VISIBLE TO ME AT CVG. WHEN I NOTICED THE ORIENTATION OF RWY 36; I KNEW I WAS OVER CVG. I WAS ABLE TO RESET THE LORAN C AND IT WAS INDICATING THAT I WAS SW OF LUK 10 NM'S; WITH A REQUIRED COURSE OF 51 DEGS TO LUK. THE CITY SKYLINE WAS INTERMITTENTLY VISIBLE THROUGH LOW CLOUD COVER. LUK TWR THEN REALIZING MY POS; VECTORED ME ALONG THE RIVER TO LUK I NOW REALIZE THAT MARGINAL WX; TURBULENCE WHICH PREVENTED ME FROM GETTING INFO FROM THE CHART; (CVG APCH FREQ); A BELIEF THAT VIS AS RPTED BY LUK WOULD ALLOW REASONABLE DEAD RECKONING; WITH VISUAL PLTING TO THE ARPT SE OF OF CINCINNATI; CONTRIBUTED TO MY NOT KNOWING WHERE I WAS. A VOR RADIAL FROM RICHMOND WOULD HAVE TAKEN ME RIGHT TO LUK; IF I HAD HAD THE WISDOM TO FLY E TO PICK IT UP. THE LOSS OF THE LORAN C AT A CRITICAL TIME; I FEEL; LED TO THE ABOVE INFRACTION.