CORPORATE ACFT FLC HAS PROB WITH MULTI FUNCTION DISPLAY DURING TAXI. THIS CAUSES A DISTR WHICH IMPACTS COMS AND AFTER RECEIVING POS AND HOLD CLRNC THEY TKOF WITHOUT CLRNC.

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WHILE TAXIING TO RWY 31R AT DAL; WE DEVELOPED A PROB WITH THE MULTI FUNCTION DISPLAY. DUE TO TSTMS IN THE AREA AND ALONG OUR RTE; WE NEEDED TO HAVE IT WORKING IN ORDER TO DISPLAY THE RADAR ON IT. WHILE TAXIING WE TRIED DIFFERENT THINGS TO GET IT BACK WHICH FOCUSED TOO MUCH ATTN TO THE PROB. UPON ARR AT THE DEP END OF RWY 31R WHILE AWAITING TKOF CLRNC; I CONTINUED TO WORK ON THE PROB SINCE THE SIC WAS NOT AS FAMILIAR WITH THE EQUIP AS I WAS. WE WERE CLRED 'INTO POS AND HOLD' WHICH WE BOTH ACKNOWLEDGED TO EACH OTHER. PRIOR TO GETTING INTO POS; THERE WAS ANOTHER XMISSION FROM THE TWR WHICH I MISSED. I ASKED THE SIC TO CONFIRM 'POS AND HOLD' AND HE SAID WE WERE CLRED FOR TKOF. I ASKED AGAIN IF WE WERE TO CONFIRM 'POS AND HOLD' AND HE SAID WE WERE CLRED FOR TKOF. I ASKED AGAIN IF WE WERE CLRED TO GO AND HE CONFIDENTLY SAID YES. AFTER ROTATION THE TWR CALLED AND SAID THAT WE HAD NOT BEEN CLRED FOR TKOF. THE SIC RPTED BACK THAT HE THOUGHT WE HAD BEEN CLRED. THE CTLR SAID WE HAD NOT; BUT THAT THERE WAS NO PROB; BUT THAT WE WERE ONLY 3 MI BEHIND THE PREVIOUS DEPARTING TFC AND TO KEEP OUR SPD BACK. CONTRIBUTING FACTORS TO THIS INCIDENT WERE DISTRS CAUSED BY MALFUNCTIONING EQUIP AND THE DIVISION OF ATTN ADDRESSING THE PROBS. THE FACT THAT ONLY 1 CREW MEMBER COULD CONFIRM OR DENY THAT TKOF CLRNC HAD BEEN ISSUED WAS A RED FLAG THAT SHOULD HAVE BEEN RECOGNIZED AND THEN RECONFIRMING WITH THE TWR ABOUT THE CLRNC.