LGT FREIGHTER CLRED FOR 180 DEG TURN ON THE RWY; CROSSES ACTIVE RWY IN PROCESS.

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THE WX WAS CLR WITH UNLIMITED VISIBILITY. WE WERE INBOUND TO CYYC AND CLRED FOR A VISUAL APCH TO RWY 34. WE WERE SWITCHED OVER TO TWR WHERE WE LEARNED THERE WAS AN ACFT ON THE RWY IN POS. HE DELAYED HIS TKOF ROLL WHICH IN TURN CAUSED US TO GO AROUND. IT WAS RATHER HURRIED BUT ALL CHKLISTS AND APPROPRIATE PROCS ACCOMPLISHED AND WE WERE REVECTORED AROUND TO LAND ON RWY 28. WE WERE CLRED TO LAND. AFTER LNDG WE WERE TOLD TO MAKE A 180 DEG TURN ON THE RWY AND TURN DOWN TXWY A. I MADE A 180 DEG TURN ON THE RWY AND PROCEEDED EBOUND ON THE RWY. WE MADE A R TURN ON WHAT WE THOUGHT WAS TXWY A; BUT IN FACT WAS TXWY C. RWY 34 INTERSECTS RWY 28 APPROX AT 9500 FT AND THE RWY IS 12675 FT LONG. AS WE WERE TURNING ONTO TXWY C; TWR ADVISED US OF IT. AFTER A FEW SECONDS I REALIZED WE HAD CROSSED RWY 34. TWR ASKED A COUPLE OF MINS LATER ABOUT XING THE RWY AND ADVISED THAT IT WAS NOT A PROB. I CALLED THE TWR AND TALKED WITH THEM BECAUSE I FELT THIS WAS A VERY POTENTIAL SERIOUS PROB. THE CTLR I TALKED TO WAS VERY APOLOGETIC ABOUT THE SLOPPY HANDLING. THEY ASSUMED WE WERE MAINTAINING 160 KTS AT THE OM WHICH WAS ASSIGNED BY APCH; WE NEVER RECEIVED THAT CLRNC. THE TWR; I HAVE NOTICED ON SUBSEQUENT TRIPS; ROUTINELY USES CROSS RWYS FOR TKOF AND LNDG. THEY ALSO PUT ACFT INTO POS AND HOLD ON THESE ACTIVE RWYS WITH XING TKOF AND LNDG TFC. WHEN WE WERE CLRED TO MAKE THE 180 DEG TURN ON THE RWY; THE TWR HAD ALREADY HAD AN ACFT INTO POS. MY FO AND I WERE CONCENTRATING ON THIS TFC AND WITH THE COMBINATION OF THE TWR NOT TELLING US TO HOLD SHORT OF RWY 34 AND VERY POOR LIGHTING ON THE TXWYS AND POOR SIGNAGE ADVISING OF THE XING RWYS; WE MISSED TXWY A AND CROSSED RWY 34 WITHOUT EVER SEEING IT. I TALKED WITH THE PARTICULAR TWR CTLR AND MENTIONED HAD WE BEEN INSTRUCTED TO HOLD SHORT OF RWY 34 WE WOULD HAVE BEEN CLUED TO THE FACT IT WAS AN ACTIVE RWY AND WOULD HAVE REACTED ACCORDINGLY. THE CTLR AGREED AND SAID THAT THERE WERE NUMEROUS COMPLAINTS FROM FLCS ABOUT THE POOR LIGHTING AT THAT PART OF THE ARPT. WITH THE TWR NOT GIVING A HOLD SHORT; AND ANOTHER ACFT WAS FACING US HEAD-ON ON RWY 28; AND THE POOR RWY LIGHTING AND TXWY LIGHTING; WE HAD DIVERTED ENOUGH ATTN AWAY FROM OUR VIGILANCE OF XING ANY RWY. THERE WAS A LIGHT TWIN ENG ACFT THAT HAD TAKEN OFF ON RWY 34 PRIOR TO OUR XING THE RWY; AND THE CTLR ASSURED ME THERE WAS NO CONFLICT; BUT THE POTENTIAL WAS SURELY THERE AND NEVER HAVING ANYTHING LIKE THIS HAPPEN IN MY 19 YRS OF FLYING; IT WAS EXTREMELY SOBERING. YOU READ ABOUT THE INSIDIOUS CHAIN OF EVENTS THAT LEAD UP TO SOMETHING LIKE THIS; AND YOU THINK IT COULD NEVER HAPPEN TO ME. I NOW KNOW BETTER. TO ADD TO THE PROB FROM NOT RECOGNIZING TXWY A; I BELIEVE AS WE MADE OUR 180 DEG TURN ON THE RWY WE WERE AT OR NEAR THE INTERSECTING POINT OF TXWY A AND RWY 28; THUS NOT PICKING UP WHERE THE TXWY ACTUALLY WAS.