A B737-300 FLC PERFORMS A RWY INCURSION WHILE FIXATED ON EQUIP PROBS AT IAH; TX.

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A TAXI UP TO AND HOLD SHORT CLRNC WAS ISSUED AT THE APCH END OF RWY 26. WHILE MOVING UP TO THE HOLD LINE; I NOTICED A 'SPD' WARNING FLAG APPEAR ON THE ADI AND ATTEMPTED TO ARM THE AUTOTHROTTLES IN PREPARATION FOR TKOF. THE AUTOTHROTTLES WOULD NOT ARM AND I BRIEFED THE FO THAT WE WOULD MANUALLY POS THE THROTTLES FOR TKOF; CLB AND CRUISE. I THEN CALLED FOR THE 'BEFORE TKOF CHKLIST.' I VISUALLY CLRED THE FINAL PRIOR TO ENTERING THE RWY AND SAW AN ACFT ON ABOUT A 10 MI FINAL; WHICH REINFORCED MY BELIEF THAT I HAD RECEIVED CLRNC ONTO THE ACTIVE RWY. AS I APCHED THE POINT ON THE RWY WHERE THE ACFT WAS BEING TURNED FOR RWY ALIGNMENT; THE CTLR INFORMED ME THAT I HAD BEEN INSTRUCTED TO HOLD SHORT. HE THEN CLRED ME FOR AN IMMEDIATE TKOF AND R TURN. A NORMAL TKOF WAS EXECUTED AND THE ACFT ON FINAL WAS NOT REQUIRED TO GO AROUND AND WAS ABLE TO LAND WITHOUT INCIDENT. CONTRIBUTING TO MY DISTR WAS THE FACT THAT I HAD TO USE EXTERNAL AIR TO START 1 ENG AT THE GATE (AN ABNORMAL PROC). OUR TAXI TO THE RWY HAD BEEN EXTRA BUSY DUE TO HAVING INOP APU PNEUMATICS WHICH REQUIRED ACCOMPLISHING ADDITIONAL CHKLISTS FOR THE SECOND ENG START AND EXTRA VIGILANCE AND EFFORT TO EXECUTE THE XBLEED START AND DELAYED ENG START PROCS WHILE TAXIING. ADDITIONALLY; THE AUTOMATIC PRESSURIZATION CONTROLLER WAS INOP; WHICH REQUIRED ACCOMPLISHING YET ANOTHER CHKLIST AND ABNORMAL PROC; WHILE TAXIING; FOR USING THE CONTROLLER IN THE STAND-BY MODE; CAUSING SOME CONFUSION FOR THE FO WHICH I ALSO HAD TO ADDRESS. BEING SO BUSY DUE TO THESE MULTIPLE ABNORMAL CONDITIONS PLUS THE UNEXPECTED AUTOTHROTTLE FAILURE AT THE RWY WERE ENOUGH DISTR TO CAUSE ME TO MISTAKENLY BELIEVE I HAD RECEIVED CLRNC ONTO THE ACTIVE RWY. I AM NOT TRYING TO CLAIM THAT THESE MULTIPLE DISTRS WERE AN ACCEPTABLE REASON FOR THIS INCIDENT; BUT NO DOUBT THEY WERE CONTRIBUTING FACTORS. I PLAN TO REDOUBLE MY EFFORTS TO REMAIN MORE AWARE OF MY SIT IN THE FUTURE. SUPPLEMENTAL INFO FROM ACN 458135: THE AIRPLANE WE HAD HAD 3 MEL'S ON IT AND 1 FOR APU PNEUMATICS INOP. THE TWR CTLR TOLD US WE WOULD BE NEXT FOR DEP. SO THE CAPT CALLED FOR THE BEFORE TKOF CHKLIST AND I BEGAN TO DO IT AS HE TAXIED THE ACFT TO THE RWY. AS I TRIED TO SOLVE IT; APPARENTLY THE CAPT WAS ALSO LOOKING AT THE PROB. BOTH PLTS HAVE TO BE DISCIPLINED IN THEIR DUTIES. THE CAPT'S IS TO TAXI AT THAT POINT; AND FO DO CHKLISTS AND TRY TO HELP WITH DIRECTIONS. IF A PROB ARISES; BOTH PEOPLE CANNOT BE 'SOLVING IT' -- THEY BOTH HAVE TO DO THEIR JOBS.