FLC OF A CESSNA CITATION II C550 FAILED TO HOLD SHORT OF RWY DURING TAXI FOR TKOF.

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I WAS DESIGNATED AS CAPT PIC (PF) OF THIS FAR PART 91 FLT. HAVING BEEN TEMPORARILY DISTR BY AN ERRONEOUS POS OF A SWITCH ON THE INST PANEL; I FAILED TO FULLY LISTEN TO THE GND CTLR'S TAXI CLRNC BEING ISSUED TO THE FO. WHEN I QUERIED THE FO HE STATED WE WERE CLRED TO TAXI TO RWY 4L. I THOUGHT I HAD HEARD THE GND CTLR MENTION SOMETHING ABOUT TXWY D; SO I HAD THE FO CONFIRM OUR CLRNC. THIS TIME THE CTLR RESPONDED WITH 'HOLD SHORT OF TXWY A;' BUT DID NOT CLARIFY THE ENTIRE CLRNC. AS WE APCHED TXWY A; THE CTLR THEN CLRED US TO 'TAXI TO RWY 4L.' AS WE PASSED TXWY D; I THEN REALIZED THAT WE SHOULD HAVE TURNED ONTO TXWY D AS CONSTRUCTION BARRICADES HAD CLOSED THE NORMAL TXWY ROUTING TO RWY 4L. THE FO CONTACTED GND CTL OF OUR 180 DEG TURN REQUIRED FOR TXWY D AND AGAIN SHE INSTRUCTED US TO 'TAXI TO RWY 4L.' THE NEW ROUTING VIA TXWY D; TXWY P; AND TXWY F CAUSED US TO CROSS RWY 4L IN ORDER TO REACH THE DEP END OF THE RWY WHICH WAS ALSO UNDER CONSTRUCTION. WE BOTH HAD APPARENTLY DEVELOPED A MIND SET THAT WE WERE CLRED ALL THE WAY TO THE DEP END OF RWY 4L AS NO 'HOLD SHORT' CLRNC WAS EVER ISSUED. AS WE APCHED THE RWY 4L INTXN ON TXWY P; I ASKED THE FO TO CLR THE RWY TO THE R; TO WHICH HE RESPONDED 'CLR ON THE R.' I STATED THAT WE WERE 'CLR L.' AS WE CROSSED RWY 4L; I DEVELOPED A VERY UNEASY FEELING AND ASKED THE FO IF HE WAS SURE WE WERE CLRED TO CROSS THE RWY. HE RESPONDED BY STATING WE HAD BEEN 'CLRED TO RWY 4L.' WHEN THE TWR CTLR ISSUED A PHONE NUMBER FOR US TO CALL; IT IMMEDIATELY BECAME CLR TO ME WHAT HAD HAPPENED. THE FO DID NOT REALIZE THAT THE CLRNC WE HAD BEEN GIVEN DID NOT ALLOW US TO CROSS THE ACTIVE RWY VIA THE NONSTANDARD ROUTING. AS SUCH; HE DID NOT CHALLENGE ME AS I TAXIED ONTO AND ACROSS THE RWY. ALTHOUGH WE WERE TECHNICALLY IN ERROR; IN A SUBSEQUENT TELEPHONE CONVERSATION WITH THE MALE GND CTLR; HE SUBMITTED THAT A 'HOLD SHORT OF RWY 4L' CLRNC WOULD HAVE BEEN APPROPRIATE; ESPECIALLY CONSIDERING THE EXTENSIVE CONSTRUCTION IN PROGRESS AND THE UNUSUAL ROUTINGS. SUPPLEMENTAL INFO FROM ACN 420048: I THEN CALLED GND TO TELL HER WE WERE TURNING AROUND TO TAXI BACK TO TXWY D. I THEN GOT A REPLY TO 'TAXI TO RWY 4L.' I THEN HEARD ANOTHER CTLR (MALE VOICE) TAKE OVER GND CTL. BEFORE WE GOT TO THE END OF THE DISPLACED THRESHOLD; GND CTL TOLD A SENECA; THAT WAS FOLLOWING US TO RWY 4L; TO HOLD SHORT OF THE RWY.