B757 CAPT MISTAKENLY STARTED TAXIING ONTO ACTIVE RWY AFTER GND HOLDING WHEN FO LOOKED UP AND NOTICED MISTAKE AND CALLED FOR STOPPING THE ACFT BEFORE IT WENT ONTO THE RWY. AFTER NOTIFYING GND CTL OF THEIR ERROR; THEY WERE GIVEN BACK-TAXI INSTRUCTIONS ON THE RWY.

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AFTER BLOCKOUT; ACFT DEVELOPED MECHANICAL. WE POSITIONED OUR ACFT ON A TERMINAL RAMP WITH ENGS RUNNING WHILE WAITING FOR MAINT PERSONNEL; TO RESPOND TO RADIO CALLS. AFTER RESOLVING MAINT PROB; IT WAS DECIDED TO CONTINUE WITH FLT. WHILE STILL PARKED; CAPT WAS TALKING TO GND ON COM #1 ABOUT WX IN THE AREA WHILE FO WAS SENDING MESSAGE TO COMPANY VIA ACARS WHILE SIMULTANEOUSLY ON COM #2 TALKING WITH LCL MAINT PERSONNEL. AT SOME POINT; CAPT ASKED GND TO CONTINUE TAXI TO RWY 25 (RFD) AND APPARENTLY DID NOT REALIZE FO WAS STILL ON COM #2 NOT LISTENING AND PREOCCUPIED WITH TYPING MESSAGE ON ACARS. WITH HEAD DOWN; FO DID NOT REALIZE ACFT WAS UNDER MOVEMENT TOWARDS ACTIVE RWY. CAPT TAXIED ACFT TOWARDS WHAT APPEARED TO BE TXWY F BUT ACTUALLY ENDED UP BEING AN ACTIVE RWY. FO LIFTED HEAD UP AND NOTICED RWY EDGE MARKINGS APCHING AND REQUESTED IMMEDIATE STOP. AT THIS POINT ACFT WAS PROTRUDING PAST THE HOLD LINE AND ENCROACHING ON RWY 25. WE NOTIFIED GND AND WAS GIVEN BACK TAXI INSTRUCTIONS AS THERE WERE NO ACFT USING THE RWY OR IN THE VICINITY. FACTORS INCLUDED: POOR TXWY MARKINGS; LIGHT RAIN; CREW NOT WORKING TOGETHER; FATIGUE (7 HR 30 MIN BLOCK FLYING NIGHT). CAPT THOUGHT THAT TAXI LIGHTS AHEAD WERE THE ENTRANCE TO TXWY F. IN FACT; IN THAT PORTION OF RAMP AREA THERE ARE NO LIGHTS SIGNIFYING OTHER EDGE OF TXWY F.