A GLF4 CREW; TAXIING FOR TKOF AT CLE; TAXIED PAST THE HOLD SHORT LINE; RESULTING IN A TWR INITIATED GAR TO LNDG TFC.

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ALTHOUGH WE HAD ALREADY RECEIVED A PDC; GND COULD FIND NO STRIP ON US; SO TAXI WAS DELAYED. WE WAITED A FEW MINS AND THEN ASKED TO START OUR TAXI AND COPY CLRNC ON THE WAY OUT. WE WERE ALLOWED TO START OUR TAXI WITH SEVERAL 'HOLD SHORT OF TXWY INSTRUCTIONS' DURING THE TAXI. DUE TO CONSTRUCTION AND OUR UNFAMILIARITY WITH THE ARPT; THE GND CTLR GAVE US PROGRESSIVE INSTRUCTIONS; AND UNABLE TO FIND OUR CLRNC; ISSUED US A NEW ONE. WE HAD DIFFICULTY READING IT BACK VERBATIM; SO 4 OR 5 ATTEMPTS WERE MADE TO CLARIFY OUR CLRNC DURING THE TAXI. THE TAXI INSTRUCTIONS HAD US TAXI ONTO A CLOSED RWY AND HOLD SHORT OF A PARALLEL RWY TO GET TO THE ACTIVE. THE CLRNC CLARIFICATION WAS INTERRUPTED SEVERAL TIMES WITH XMISSIONS BTWN OTHER ACFT; AND WE STILL WERE CLARIFYING THE CLRNC ENTERING THE CLOSED RWY. WHILE TRYING TO COPY OUR CLRNC; ACCOMPLISH REQUIRED CHKLISTS; AND FOLLOW GND'S INSTRUCTIONS; WE INADVERTENTLY TAXIED JUST OVER THE HOLD LINE FOR THE RWY WE HAD BEEN INSTRUCTED TO HOLD SHORT OF (RWY 24L). AS SOON AS WE REALIZED OUR ERROR; WE STOPPED; AND AVOIDED ENTERING THE RWY DIMENSIONS. WHILE WAITING FOR A BREAK IN THE RADIO CHATTER TO ALERT THE CTLRS; WE WERE TOLD WE HAD TAXIED ONTO A RWY AND AN ACFT HAD BEEN SENT AROUND. SHORTLY AFTER; WE CONTACTED TWR AND WERE CLRED FOR TKOF ON RWY 24L AND INSTRUCTED DURING CLBOUT TO CONTACT CLEVELAND TWR AFTER LNDG. AS SOON AS WE ARRIVED AT OUR DEST; I MADE THE CALL AND DISCUSSED THE INCIDENT WITH TRACON AND TWR. I BELIEVE THE CONSTRUCTION; CROWDED FREQ; AND EXTENDED CONFUSION OVER OUR CLRNC ALL CONTRIBUTED TO MY ERROR.