EMB145 FLT CREW LINES UP ON WRONG RWY AT DFW AFTER LATE RWY CHANGE.

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THE ACTUAL EVENT WAS THAT THE PF VISUALLY LINED UP WITH A PARALLEL BUT INCORRECT RWY DURING A VISUAL APCH. DURING APCH PHASE OF FLT (APPROX 25 MILES OUT) WAS ASSIGNED TO RWY 35C AT DFW ARPT. FLT PROCEEDED NORMALLY UNTIL WELL INTO THE DOWNWIND PHASE (SE OF ARPT); WHEN WE WERE HANDED OFF FROM APCH CTLR ON FREQ 119.4 TO CTLR ON FREQ 127.07. I BELIEVE THIS HANDOFF WAS LATE AND BEGAN THE SEQUENCE OF EVENTS. WERE GIVEN A 200 DEG HEADING AND WAS REASSIGNED TO RWY 36L. THIS WAS FAVORABLE TO THE CREW BECAUSE OUR ARR TERMINAL WAS ON THE W SIDE OF ARPT; BUT ALSO PUT BOTH PLTS TO WORK IMMEDIATELY RESETTING OUR FMS EQUIPMENT AS WELL AS NAV RADIOS FOR THE NEW RWY. DURING THIS REPROGRAMMING WE WERE GIVEN A 270 DEG HEADING AND ASKED IF WE HAD THE ARPT IN SIGHT. WE ACKNOWLEDGED THE HEADING AND THE AIRPORT IN SIGHT AND WAS CLEARED FOR THE VISUAL APCH TO RWY 36L; AND TO CONTACT TWR ON 124.15. THE PNF CONTACTED THE TWR AND THE PF SET THE AUTOPLT TO DSND TO THE IAF ALT OF 2300 FT. AS THE PF MY HEAD WAS 'UP AND DOWN' SEVERAL TIMES DURING THE DSCNT TO 2300 FT ACCOMPLISHING REPROGRAMMING TASKS ETC. BY THE TIME WE LEVELED AT 2300 FT I WAS READY TO TAKE OVER VISUALLY FOR THE APCH. I DISCONNECTED THE AUTOPLT AND BEGAN THE BASE TO FINAL TURN TO WHAT I THOUGHT WAS RWY 36L; SHORTLY AFTER THE ROLLOUT; THE TWR OPERATOR CALLED AND SAID 'IT LOOKS LIKE YOU'RE LINED UP WITH RWY 35L.' IT ONLY TOOK SECONDS TO REALIZE THE MISTAKE AND ACKNOWLEDGED SO. HE THEN SAID 'I CAN GET YOU RWY 36R IF YOU WANT IT;' WE ACCEPTED AND MADE A JOG TO OUR L PUTTING US ON ABOUT A 2.5 TO 3 MILE FINAL FOR RWY 36R; AND LANDED WITHOUT INCIDENT.