MD80 CREW HAD RWY INCURSION AT ORD.

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POSSIBLE RWY INCURSION. LEAVING GATE AT ORD. GND GAVE DIRECTIONS TO RWY 4L; L ON TXWYS B; P; H; AND E. WHILE ON TXWY H; APCHING TXWY A; GND SAID HOLD SHORT OF RWY 4L ON TXWY E; MONITOR TWR. I CROSSED RWY 4L TO CONTINUE TO TXWY E. AFTER WE CROSSED RWY 4L TWR CALLED US. THE FO; WHO HAD BEEN OFF THE FREQ AND ON THE INTERCOM; ANSWERED; SAYING WE THINK WE MADE A WRONG TURN TO RWY 4L. TWR THEN SAID HOLD SHORT OF RWY 4L ON TXWY E. NOTHING MORE WAS SAID FROM TWR. THE DIRECTIONS I DESCRIBED FROM GND ON INITIAL CONTACT ARE WHAT I HEARD; WROTE DOWN AND THE FO CONFIRMED WITH GND. ON READBACK TO GND THERE WAS NO RESPONSE LEADING US TO PROCEED AS DIRECTED. LOOKING AT THE ARPT DIAGRAM; IT MAKES MORE SENSE TO APCH RWY 4L FROM THE S OF TXWY E; BUT I BELIEVE WE TAXIED AS DIRECTED. THERE WAS AN ACFT OCCUPYING THAT POS ON TXWY E AND NO ROOM FOR ANOTHER ACFT. AN ADDITIONAL FACTOR WAS FO WAS OFF FREQ AT A CRITICAL TIME DISCUSSING A PAX PROB WITH A FLT ATTENDANT. THERE WERE NO ACFT TAKING OFF OR LNDG ON RWY 4L AT THE TIME AND THERE WERE NO OTHER ACFT TAXIING NEAR OUR POS AT THE TIME. SUPPLEMENTAL INFO FROM ACN 482739: GND CTL GAVE US TAXI INSTRUCTIONS COUNTER-CLOCKWISE FLOW TO RWY 4L. WE THOUGHT THE INSTRUCTIONS WERE TXWYS B; P H; E TO RWY 4L. AS WE TURNED WBOUND ON TXWY H; FLT ATTENDANT #1 CALLED US WITH A PAX PROB. I LISTENED TO THE PROB; AND THEN RELAYED THE INFO TO THE CAPT. WE DISCUSSED THE PROB AND THEN I RELAYED THE SOLUTION FOR THE PAX BACK TO FLT ATTENDANT #1. AFTER HANGING UP THE PHONE; I GOT MY BEARINGS AND REALIZED WE WERE TAXIING ACROSS RWY 4L ON TXWY H. I DO NOT THINK WE WERE SUPPOSED TO TAXI ACROSS RWY 4L L TO GET TO THE END OF THE RWY; BUT WERE SUPPOSED TO TAKE TXWY H TO TXWY A TO TXWY E TO RWY 4L. THE CAPT HAD BEEN HANDED OFF TO TWR WHILE I WAS ON THE PHONE. AFTER XING RWY 4L; THE TWR CALLED US AND TOLD US TO TURN L ONTO TXWY E FOR RWY L. THERE DID NOT APPEAR TO BE A CONFLICT WITH ANY OTHER ACFT WHEN WE TAXIED ACROSS RWY 4L. I FEEL THIS POSSIBLE INCURSION WOULD NOT HAVE HAPPENED IF WE HAD NOT BEEN INTERRUPTED WITH THE PAX PROB. ALSO; IT WAS A NON STANDARD TAXI TO RWY 4L; AS WE USUALLY TAXI CLOCKWISE ON ORD OUTBOUNDS.