BE1900D ACFT ON APCH TO PARALLEL RWYS PF; CAPT; THINKS CLRNC TO LAND ON THE L RWY; BUT THE CLRNC WAS FOR THE R.

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WE WERE FLYING AN ACFT WITH FLAPS WHICH WERE MELED (IE; NO FLAPS). UNDER THE MEL WE CANNOT SILENCE THE GEAR WARNING HORN WHICH IS ACTIVATED ANYTIME THE PWR LEVERS ARE BROUGHT BELOW 84%-86% TO N1 AND IN THIS PARTICULAR ACFT THE HORN CAME ON BELOW 88%-89% N1; (PWR SETTINGS BELOW THIS LEVEL ARE REQUIRED FOR A TYPICAL APCH PROFILE). OUR TCASII SYS WAS ALSO INOP AND ON MEL WHICH HELPS US WITH SITUATIONAL AWARENESS IN THE APCH ENVIRONMENT. THE FO PICKED UP THE ATIS WHICH INDICATED THAT RWY 10R WAS IN USE FOR ARRS. DUE TO THE FLAP MEL WE HAVE TO RUN A 'NO FLAP' CHKLIST AFTER OUR APCH CHKLIST. I DECIDED TO GET THE CHKLISTS DONE EARLY SO WE WOULD NOT NEED TO RUSH THROUGH THEM WHILE ON APCH. WE COMPLETED THE IN RANGE CHKLIST FIRST (ABOUT 40-50 MI OUT) WHICH INCLUDES THE APCH BRIEFING. SINCE THE ATIS INDICATED RWY 10R WAS IN USE I SET THE RADIOS/ALT/ETC; FOR A VISUAL TO RWY 10R BACKED UP BY THE ILS RWY 10R CMH WHICH INCLUDED A FULL BRIEFING FOR THE ILS. ATC CONTINUED TO VECTOR US TO A BASE LEG AND HAD US AT 6000 FT VERY CLOSE TO THE ARPT AND THEN DSNDED US TO 5000 FT. WE THEN COMPLETED THE APCH CHKLIST AND STILL HAD NOT RECEIVED AN INSTRUCTION ON WHICH RWY TO EXPECT (THE APCH CHKLIST INCLUDES TUNING AND IDENTING RADIOS WHICH WERE SET FOR RWY 10R PER ATIS). I HAD THE ARPT IN SIGHT WHEN ATC ASKED US IF WE HAD THE FIELD. WE RESPONDED AFFIRMATIVE AND WERE CLRED FOR WHAT I BELIEVED WAS A VISUAL TO RWY 10R (ATC AND FO LATER THOUGHT RWY 10L) AND WERE INSTRUCTED TO FOLLOW A CESSNA WHICH WAS ON BASE LEG FOR THE RWY (TCASII INOP AND WE WERE LOOKING FOR TFC). THE REASON FOR THIS ASSUMPTION WAS THE ATIS SAID RWY 10R (WHICH HAD BEEN BRIEFED AND SET-UP EARLIER BY ME) AND THE POS WE WERE IN FOR RWY 10R WAS A STANDARD TURN FROM BASE TO FINAL (SEE ILLUSTRATION). THE CTLR ALSO HAD US VERY HIGH WHEN THE CLRNC WAS RECEIVED (5000 FT ON 5-7 MI FINAL; ARPT ELEVATION 815 FT) AND EVEN ASKED US IF WE HAD ENOUGH ROOM TO GET DOWN. WE TOLD HIM WE WOULD GIVE IT OUR BEST SHOT AND I BEGAN THE TURN TO FINAL (WE WERE RUNNING LATE OUT OF CLE DUE TO A MAINT DELAY). ONCE ESTABLISHED ON FINAL WE CONTACTED THE TWR AND THEY CLRED US TO LAND ON RWY 10R (NO CTLR EVER SAID YOU APPEAR TO BE LINED UP ON THE WRONG RWY). WE HAD TO MAKE A PWR REDUCTION TO FLT IDLE WHEN CLRED FOR THE APCH IN ORDER TO GET DOWN (AND I HAD EARLIER CALLED FOR PROPS TO MAX TO HELP SLOW TO GEAR SPD OF 180 KIAS AND WE ONLY SLOWED TO 190 KIAS DUE TO HIGH N1 TRIP ON THIS ACFT). THE GEAR HORN WAS SOUNDING LOUDLY AS THE SPD BLED OFF TO 180 KIAS AND BELOW UPON WHICH I CALLED GEAR DOWN AND THE HORN SILENCED. THE NO FLAP CHKLIST AND THE LNDG CHKLIST WERE THEN COMPLETED ON FINAL WHICH MEANT THINGS WERE VERY BUSY AS WE WERE TRYING TO GET ACFT DOWN; TALK TO ATC; RUN CHKLISTS; ETC. (THESE CHKLISTS CAN'T BE COMPLETED UNTIL THE GEAR IS LOWERED.) ON ABOUT A 1 MI FINAL THE FO ASKED ME IF WE WERE SUPPOSED TO BE ON RWY 10L; I TOLD HIM TO VERIFY WITH ATC THAT WE WERE CLRED TO LAND ON RWY 10R AND TWR CONFIRMED THAT WAS CORRECT. AFTER TAXIING CLR OF RWY TWR ASKED IF WE WERE CLRED FOR A VISUAL TO RWY 10L. THE FO RESPONDED BY SAYING THAT WE WERE ALSO DISCUSSING THIS ITEM; THE TWR CTLR THEN RESPONDED BY SAYING HE SAW US LINED UP FOR RWY 10R AND CLRED US TO LAND RWY 10R. I ASKED IF WE NEEDED TO CALL THEM TO DISCUSS THE ISSUE FURTHER AND HE NICELY SAID; 'NO; DON'T WORRY ABOUT IT' (OR SOMETHING TO THIS EFFECT). CONTRIBUTING FACTORS: 1) ATC VECTORS TO A VERY HIGH APCH AND PAST FINAL FOR RWY 10L. 2) RWY 10R BEING USED FOR LNDGS WAS RPTED ON ATIS. 3) HIGHER PLT WORKLOAD DUE TO FLAPS INOP AND TCASII INOP. 4) LOSS OF SITUATIONAL AWARENESS DUE TO TCASII INOP AND COULD NOT TRACK ACFT WE WERE TO BE FOLLOWING. 5) HUMAN FACTORS -- MY HEARING THE RWY I THOUGHT WAS LOGICAL (POS/ATIS/ETC) INSTEAD OF THE ONE CLRED FOR. HOW IT WAS DISCOVERED: FO QUESTIONING ME ON APCH; CONFUSION BECAUSE CLRED FOR VISUAL RWY 10L; BUT CLRED TO LAND RWY 10R. CORRECTIVE ACTION: HAD FO QUESTION ATC ON SHORT FINAL AND VERIFIED CLRED TO LAND RWY 10R. ATC VERIFIED WE WERE CLRED TO LAND RWY 10R. I WAS MENTALLY PREPARED TO EXECUTE A GAR IF NEEDED. CORRECT SIT: ATC COULD HAVE TOLD US WHICH RWY TO EXPECT EARLIER IN THE APCH SEQUENCE; AND COULD HAVE VECTORED US FOR A LONGER FINAL TO HAVE A BETTER DSCNT PROFILE. I COULD HAVE LISTENED TO ATC INSTRUCTIONS MORE CAREFULLY INSTEAD OF CONTINUING FOR WHAT I WAS 'SET UP' TO DO AND WHAT SEEMED LOGICAL; TCASII AND FLAPS COULD HAVE BEEN OPERATIVE WHICH WOULD HAVE GREATLY DECREASED PLT WORKLOAD AND INCREASED SITUATIONAL AWARENESS.