KINGAIR 200 FLT CREW MAKES A TKOF WITHOUT CLRNC AT JFK.

Narrative

WE WERE IN A KING AIR 200 AND I WAS PIC AND I HAD A SIC DOING THE RADIOS. WE WERE AT JFK LEAVING THE GA RAMP WITH 2 PAX. THERE WERE SEVERE TSTMS COMING IN FROM THE W ALONG OUR RTE OF FLT WHICH WAS TO MVY. THERE WERE A LOT OF DELAYS AT THE ARPT WITH ACFT TAXIING AND SITTING ALL OVER THE PLACE. GND CTL WAS VERY BUSY. WE RECEIVED THIS QUESTION FROM GND: 'CAN YOU GET TO RWY 13R VIA PE?' WE SAID WE COULD; AND HE TOLD US TO 'TAXI TO RWY 13R VIA PE.' HE DID NOT SAY 'R ON Q AND L ON PE TO HOLD SHORT OF 13R' WHICH IS NORMAL FOR US AT MOST LARGE ARPTS. IT WAS CONFUSING BUT WE FOUND PE AND WHEN WE GOT ON IT THERE WAS ANOTHER ACFT AT R ANGLES TO US ON P. WE STOPPED TO ALLOW THIS OTHER ACFT TO GET TO RWY 13R AS WE WERE NOT SURE WHAT WAS GOING ON BECAUSE ALL THE ACFT WE SAW WERE TAXIING DOWN RWY 13R TO GET TO OTHER LOCATIONS AND NOT TAKING OFF. WE WERE TOLD TO GO TO TWR FREQ. WE DID AND HE TOLD US 'POS AND HOLD RWY 13R' IN A TONE THAT SUGGESTED WE WERE GOING TO TAKE OFF RIGHT AWAY. BEING SO FAR BACK FROM THE HOLD SHORT LINE OF RWY 13R; I WAS RUSHING TO GET ONTO THE RWY; GET THE CHKLIST COMPLETE; AND AT THE SAME TIME I WAS TRYING TO GET THE RADAR TO COME UP BECAUSE IT SEEMED TO BE AFFECTED BY THE HEAT AND WOULD NOT 'BOOT UP.' I THOUGHT I HEARD THE TWR SAY 'ACFT X CLRED FOR TKOF; FLY HDG OF 285 DEGS' AND I THOUGHT I HEARD MY SIC READ THAT BACK. SO I TOOK OFF. THE SIC DID HIS NORMAL DUTIES ON THE TKOF ROLL. RIGHT AS I BROKE GND THE TWR ASKED IF WE COULD MAKE OUR ASSIGNED TURN TO HDG 285 DEGS BEFORE RWY 22R. THE SIC REPLIED YES AND I INITIATED THE TURN AS REQUESTED WITH NO PROB. IT WAS AT THIS TIME THAT THE TWR STARTED YELLING; 'I DID NOT CLR YOU TO TAKE OFF.' MY SIC REPLIED THAT HE THOUGHT HE DID. THE TWR SAID 'WELL YOU THOUGHT WRONG.' THE TWR TURNED US OVER TO DEP AT THIS TIME. WHEN WE TRIED TO CONTACT DEP; MY SIC COULD NOT DO SO WITH HIS RADIO. I DON'T KNOW WHY BUT I HAD TO DO THE COMS FOR THE NEXT FEW MINS. REASONS FOR THIS INCIDENT: 1) I THINK THE TWR ACTUALLY TOLD US 'AFTER TKOF' AND NOT 'CLRED FOR TKOF.' 2) THE CTLRS AT JFK GIVE UNORTHODOX DIRECTIONS. 3) BEING RUSHED BY ALL THE EVENTS MENTIONED ABOVE.