DISTR ACR CREW TAXIES ACROSS AN ACTIVE RWY WITHOUT CLRNC.

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A CLR CASE OF DISTR ON MY PART AGGRAVATED BY POOR PRIORITIZING OF DUTIES. JUST AFTER ENG START; WE WERE CLRED TO 'TAXI TO RWY 14L; L ON TXWY B; TXWY J; CROSS RWY 9L.' AS WE BEGAN TO MOVE; I POSITIONED THE FLAPS TO TKOF SETTING AND JUST THEN THE CABIN CREW CALL SIGNAL ILLUMINATED ALONG WITH A CHIME. THE PURSER RPTED THAT SHE WAS HAVING TROUBLE WITH A PAX WHO INITIALLY REFUSED TO TURN OFF HIS CALCULATOR AND THEN WOULD NOT CHANGE SEATS WHEN REQUESTED. HIS SEAT WOULD NOT STAY UPRIGHT AND HE WAS BLOCKING AN EXIT ROW. I ADVISED HER TO TELL THE PAX THAT THE CAPT REQUESTED THAT HE MOVE FOR SAFETY PURPOSES AND THE ONLY ALTERNATIVE WOULD BE A RETURN TO THE GATE. UPON FINISHING THAT CONVERSATION; I NOTICED THAT WE HAD AN INDICATION OF AN AIR CONDITIONING MALFUNCTION IN THE R SYS. I POINTED THIS OUT TO THE CAPT AND SAID I WOULD CHK THE MANUAL FOR PROCS TO CLR THE PROB. I GOT THE MANUAL OUT; FOUND THE PAGE AND PROCEEDED WITH THE AIR CONDITIONING RESET PROC; WHICH CLRED THE FAULT INDICATION. AT SOME POINT IN THIS PROCESS I LOOKED UP FORWARD AND WE WERE ABOUT TO CROSS A RWY. THE CAPT MADE A COMMENT ABOUT EITHER 'TXWY B' OR 'TXWY J' AND I REMEMBERED THAT WE HAD BEEN CLRED TO CROSS RWY 9R. A LITTLE LATER; GND CTL CALLED AND SAID; 'I WANTED YOU TO STAY ON TXWY B; YOU JUST CROSSED AN ACTIVE RWY.' WE HAD LEFT TXWY B; GONE STRAIGHT ON TXWY H; AND CROSSED RWY 22L WHICH WAS IN USE FOR LNDG TFC. GND SAID; 'NO PROB; THE CLOSEST TFC WAS ON A 2 MI FINAL.' I SHOULD HAVE ASKED TO HAVE THE ACFT STOPPED TO RESOLVE THE PAX ISSUE; AND SINCE THE TAXI TO RWY 14L WAS LONG THERE WAS PLENTY OF TIME TO DELAY THE AIR CONDITIONING RESET UNTIL A LESS CONGESTED TAXI AREA. MY ATTN TO THE MOST IMPORTANT DETAIL; SAFE OP OF THE ACFT; WAS IMPAIRED BY MINOR EVENTS OCCURRING TOGETHER. SUPPLEMENTAL INFO FROM ACN 446250: TAXI INSTRUCTION: TAXI ON TXWY B TO TXWY J FOR RWY 09L. (YOU CAN'T TAXI FROM TXWY B TO TXWY J UNLESS YOU MAKE A R TURN ON TXWY A3 TO TXWY J.) ON THE WAY OUT; TAXIING ON TXWY B; THE FO GOT BUSY WITH CABIN PROB AND COMPANY COM FOR WTS; WHILE THE CAPT TAXIED ON TXWY B; TXWY H; STRAIGHT AHEAD TOWARDS RWY 09L INTXN J; XING RWY 22R/4L WHICH WAS ACTIVE; BUT DID NOT INTERFERE WITH TFC AT THE TIME OF XING. CONTRIBUTING FACTORS: INCOMPLETE AND CONFUSING TAXI INSTRUCTIONS; FREQ; GND CTL CONGESTION; CABIN PROBS.