RPTR CAPT; WITH A PROB FO; BECAME DISTRACTED WHILE TAXIING AND CROSSED THE ACTIVE RWY WHERE HE HAD BEEN INSTRUCTED TO HOLD SHORT.

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ON THE FIRST LEG OF A 2-DAY TRIP WITH A NEW CREW (I DID NOT KNOW ANY OF THE CREW MEMBERS). OUR ACFT WE PICKED UP HAD A STALL WARNING FAILURE AND MAINT WAS WORKING ON THE ACFT. FO WAS LATE AND I DID THE WALKAROUND. MAINT TOLD US THE ACFT HAD TO GO TO THE HANGAR AND WE GOT A NEW ACFT AT A NEW GATE. RUSHED OVER TO THE NEW ACFT CALLED DISPATCH AND GOT A NEW RELEASE/FLT PLAN. CALLED CATERING; TWR (COMPANY) TO GET FUEL AND ADVISE BAGGAGE HANDLERS. RETURNED TO THE COCKPIT TO FIND THE FO READING A PAPER AND ASKED HIM HOW IT WAS GOING. HE SAID THE ACARS COULDN'T GET THE CLRNC BUT HE THOUGHT HE KNEW THE CLRNC. I EXPLAINED TO HIM ONCE YOU RECEIVED THE ATC CLRNC OVER THE ACARS YOU CANNOT GET IT AGAIN. I HAD HIM CALL CLRNC AND HE GOT A PARTIAL CLRNC DUE TO HIS POOR VERBAL SKILLS. I HAD TO LEAVE THE COCKPIT TO GET THE FUEL SLIP AND CHK ON WHY THE BAGGAGE PEOPLE NEVER SHOWED. FINALLY RETURN TO COCKPIT TO RUN CHKLIST (FO WAS READING AGAIN). ON PUSHBACK AND START; FO DIDN'T DO HIS FLOWS PROPERLY AND I HAD TO DO IT FOR HIM (HE ALSO WAS NOT WEARING HIS SHOULDER HARNESS AND HAD RESPONDED ON SO I WAS REALLY WEARY OF HIS ATTN TO DETAIL. OUR TAXI INSTRUCTION CAME WHEN I WAS DISTRACTED AND HE THEN LEFT THE FREQ TO GET A NEW CLRNC AS INSTRUCTED BY GND. HE COULD NOT REMEMBER OUR CALL SIGN AND AS I CORRECTED HIM AND LISTENED TO THE CLRNC; I CROSSED RWY 28C INSTEAD OF TAXIING TO IT. I OVERLOADED MYSELF; DID NOT CTL THE ACFT IN STRICT COMPLIANCE WITH ATC INSTRUCTION DUE TO MY CONFUSION AND FEELING RUSHED TO THE POINT THAT I MOVED THE ACFT WITHOUT BEING ABSOLUTELY SURE OF THE TAXI RTE.