RPTR ORIENTS ACFT FOR THE WRONG RWY.

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UPON COMPLETING 2 1/2 DAYS OF RECURRENT GND SCHOOL; THE CREW WAS ASKED TO VOLUNTEER TO DEADHEAD TO LIT TO FERRY A BAE 3201 TO BNA. THE ACFT HAD UNDERGONE SOME 'HEAVY' MAINT AND HAD WAITED 3 DAYS TO BE RETURNED TO HOME BASE. DURING THE 'AFTER-START' CHKLIST; WE NOTED THE R HSI AND L RMI BOTH HAD RED FLAGS; DENOTING A SINGLE COMPASS FAILURE. WE ALSO HAD A FLT DATA RECORDER LIGHT WHICH INDICATES IT WAS INOP. WE RESET THE CIRCUIT BREAKERS FOR ALL DISCREPANCIES; BUT FAILED TO CORRECT THE ABNORMALITIES. I ELECTED TO CONTINUE SINCE IT WAS A CLR VFR NIGHT AND ALL OTHER SYS CHKED GOOD. WE ASKED FOR AN ILS TO RWY 22L WITH A MISSED APCH AND REENTER FOR A VISUAL TO RWY 18. APCH CTL RECOMMENDED A CIRCLE FROM RWY 22L TO RWY 36. WE AGREED AND THE CTLRS IN BOTH 'APCH' AND 'TWR' WERE VERY COOPERATIVE. I DSNDED TO THE MDA (880 FT MSL) ON THE ILS AND OVER RWY 22L TURNED SLIGHTLY L FOR A R DOWNWIND FOR RWY 36. I NOR THE FO HAD POSITIVELY IDENTED RWY 36; BUT WE COULD EASILY DISTINGUISH RWY 4L- 22R AND THE THRESHOLDS WERE ADJACENT. THIS WAS THE FIRST TIME THE FO HAD BEEN TO LIT AND MY SECOND. TWR CLRED US TO CIRCLE AND LAND ON RWY 36. I ASKED THE FO TO HELP BY CALLING THE BASE TURN. HE ACKNOWLEDGED AND CALLED MY ATTN TO SOME ANTENNAS. IN THE CONFUSION OF SEVERAL DISTRACTING FACTORS: AN INOP GYROSCOPE ON THE FO'S SIDE; AND THE PERCEIVED GREATER INTENSITY OF THE RWY 4L-22R LIGHTS: WE BOTH MISIDENTED RWY 4L AS RWY 36. WHEN I REALIZED THE ERROR I WAS OUT OF POS TO MAKE A SAFE; STABILIZED APCH TO RWY 36; THEREFORE ELECTED TO GAR. TWR ADVISED TO ENTER A L BASE FOR RWY 18; BUT AGAIN I WAS NOT IN A POS TO MAKE A SAFE APCH AS I HAD RAISED THE GEAR AND FLAPS. TWR ASKED US TO TURN TO 220 DEGS FOR A SUBSEQUENT VECTOR FOR A VISUAL TO RWY 18. THERE WERE SEVERAL CONTRIBUTING FACTORS TO THE CAUSE WHICH I BELIEVE WAS LACK OF POS IDENT OF THE RWY TO WHICH WE WERE CIRCLING. WE WERE TIRED; WE HAD A GYROSCOPE COMPASS INOP ON THE FO SIDE; THE FO WAS NEW TO THE ARPT; AND THE TWR CTLR WAS ATTEMPTING TO MELD US INTO OTHER TFC WHICH WAS LNDG IN THE OPPOSITE DIRECTION. HAD WE BEEN MORE FAMILIAR WITH THE ARPT; AND HAD IT BEEN DAYLIGHT RATHER THAN DARK; THE CONFUSION AND MISIDENT SHOULD NOT HAVE OCCURRED. I BELIEVE MY DECISION TO GAR AFTER MISIDENTING THE RWY WAS CORRECT. TO PREVENT A RECURRENCE WILL REQUIRE GREATER ATTN TO DETAIL THAN WE GAVE THE 'CIRCLE TO LAND' ON RWY 36 FROM THE ILS TO RWY 22L. WE DID DISCUSS IT; BUT IT JUST DID NOT LOOK THAT DIFFICULT.