A B734 CREW MISSED TURN TO TKOF RWY; CONTINUED AN UNAUTH TAXI ACROSS AN INTERSECTING RWY.

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TWR/GND CTL INSTRUCTED US TO TAXI TO RWY 11L AT A4. THE CAPT STARTED TO TAXI AND I WENT HEADS DOWN TO PROGRAM THE FMS. THEN AS I WAS BRIEFING THE DEP; I DISCOVERED I DIDN'T PUT MAX PWR IN THE FMS AS WAS REQUIRED DUE TO THE DEICE PROC JUST ACCOMPLISHED. I THEN SELECTED MAX PWR WHICH DELETED OUR PROGRAMMED TKOF V-SPDS. THE CAPT TRYING TO HELP THEN WENT HEADS DOWN TO REINSERT THE V-SPDS WHILE I WAS DOING OTHER PROGRAMMING. I THEN LOOKED UP TO SEE US XING RWY 3/21. THIS PUZZLED ME BECAUSE I THOUGHT OUR INTXN A4 WAS PRIOR TO RWY 3/21; BUT I WAS NOT VERY FAMILIAR WITH THIS ARPT AND THE CAPT WAS; ALTHOUGH IT HAD BEEN SOME YRS SINCE HE'D BEEN HERE. BY THIS TIME WE'D ALREADY CROSSED THE RWY. I TOLD THE CAPT THAT I THOUGHT WE'D PASSED OUR INTXN AT ABOUT THE SAME TIME THAT HE REALIZED IT. WE THEN GOT CLRNC FROM GND/TWR (SAME PERSON WORKING BOTH) TO TAXI BACK ON RWY 3/27 TO RWY 11L FOR TKOF. FROM NOW ON; IF THE CAPT STARTS PROGRAMMING THE FMS; I WILL GO HEADS UP AND STOP PROGRAMMING. EVEN THOUGH THAT PROGRAMMING IS MY DUTY; I MAY HAVE BEEN ABLE TO PREVENT AN UNAUTH RWY XING AND POTENTIAL DISASTER HAD I DONE THAT. I COULD ALSO BE MORE ASSERTIVE IN TELLING THE CAPT THAT I WILL PROGRAM; HE SHOULD TAXI. SUPPLEMENTAL INFO FROM ACN 497965: ON TAXI OUT WE WERE BUSY WITH THE TAXI CHKLIST. A CHANGE TO THE FMC WAS REQUIRED AND I WENT HEADS DOWN TO INPUT THE CHANGE; WHICH I SHOULD NOT HAVE DONE. WITH THE RWY LAYOUT; I MISSED THE TURN AT A4 AND INADVERTENTLY CROSSED RWY 21/3. AT THAT TIME THE GND CTLR AUTH A TURN ONTO RWY 21 AND RWY 11L.