FLC OF LTT CROSSED RWY 17-35 WITHOUT CLRNC WHILE TAXIING FOR DEP.

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THE FO CONTACTED GND CTL FOR TAXI CLRNC AS I WAS TAXIING THE ACFT AWAY FROM THE GATE. MOST OF MY ATTN AT THIS TIME WAS FOCUSED ON THE RAMP AGENT'S HAND SIGNALS SINCE I WAS DEPARTING THE RAMP AREA AT NIGHT. AS A RESULT; I MISSED THE GND CTLR'S TAXI INSTRUCTIONS. I ASKED THE FO IF WE HAD BEEN ASSIGNED RWY 27R; CONSIDERING THAT WAS THE RWY WE LANDED ON 20 MINS PRIOR. HE SAID HE THOUGHT WE WERE GOING TO RWY 27L BUT HE WOULD VERIFY THE CLRNC WITH GND. AT THIS POINT WE WERE ON TXWY H AND I STOPPED THE ACFT UNTIL WE COULD CONTACT GND FOR CLARIFICATION. THE GND CTLR INSTRUCTED US TO TAXI VIA TXWY H; TXWY E; AND HOLD SHORT OF RWY 27R; EXPECT RWY 27L FOR DEP. I ASKED THE FO IF HE SAW ANY SIGNS FOR TXWY E ON HIS SIDE OF THE ACFT SINCE I DID NOT SEE ANY ON MINE; AND HE SAID NO. AS I STARTED TAXIING STRAIGHT AHEAD ON TXWY H; I ASKED THE FO TO LOCATE TXWY E ON THE ARPT DIAGRAM. HE INDICATED THAT TXWY E SHOULD BE TO OUR R ON TXWY H. AT THIS POINT WE CONTINUED WITH THE TAXI CHKLIST AND BECAME DISTR; WHICH RESULTED IN US INADVERTENTLY XING RWY 17/35 ON TXWY H. I STOPPED THE ACFT AS SOON AS I COULD SINCE WE BOTH REALIZED AT THIS TIME THAT WE HAD MISSED TXWY E. THE GND CTLR ALSO MENTIONED AT THIS TIME THAT WE HAD MISSED TXWY E AND HAD CROSSED RWY 17/35. THE CTLR INSTRUCTED US TO CONTINUE STRAIGHT AHEAD ON TXWY H AND HE WOULD CHANGE OUR DEP RWY TO RWY 27R. AFTER TALKING TO THE TWR; I WAS TOLD THIS EVENT PRESENTED NO PROB FOR THEM AND THAT NO OTHER ACFT WERE AFFECTED. AFTER DISCUSSING THIS FURTHER WITH THE FO; WE DETERMINED THIS EVENT WAS PRIMARILY DUE TO US RUNNING BEHIND SCHEDULE AND RUSHING IN AN ATTEMPT TO MAKE UP SOME TIME. OUR 18 MIN TURNAROUND IN PHILADELPHIA WAS AN INADEQUATE AMOUNT OF TIME IN THIS SIT FOR US TO ACCOMPLISH EVERYTHING WE NEEDED; INCLUDING A MORE THOROUGH PREFLT BRIEFING.