BE200 CREW HAS RWY INCURSION AT FXE.

Narrative

COPLT RECEIVED ATIS AND IFR CLRNC ON GA RAMP ON SW SIDE OF ARPT. COPLT WAS HAVING TROUBLE WITH PUSH TO TALK SWITCH. GND CTL GAVE TAXI INSTRUCTIONS TO RWY 26 WITH HOLD SHORT OF RWY 31. COPLT READ BACK INSTRUCTIONS AND HOLD SHORT RWY 31. COPLT HAD TAXI DIAGRAM AND WAS PROVIDING PROGRESSIVE INSTRUCTIONS TO ME. GND CTL UPDATED TAXI INSTRUCTIONS TO HOLD SHORT OF TXWY DUE TO TFC THEN CONTINUE AFTER TFC PASSED AND HOLD SHORT OF RWY 31. COPLT STILL HAVING DIFFICULTY WITH PUSH TO TALK AND PUT DOWN TAXI DIAGRAM. AFTER MAKING TURN TOWARD RWY 31; I REACHED FOR TAXI DIAGRAM TO VERIFY OUR LOCATION. IN CONFUSION I ALLOWED ACFT TO PASS OVER HOLD SHORT LINE. I IMMEDIATELY STOPPED ACFT AND AT THE SAME TIME HEARD GND CTL SAY NXXXXX STOP; NXXXXX STOP. I ALSO OBSERVED A BEECH BONANZA MAKE A R TURN OFF OF RWY 31 AS IF HE HAD ABORTED TKOF. GND CTLR ADVISED TO CALL TWR DUE TO POSSIBLE PLTDEV. THE EVENTS THAT LEAD TO THIS WERE COPLT DISTR BY PUSH TO TALK PROB; BUSY ARPT AND THAT I REALIZED HIS DISTR TOO LATE. I SHOULD HAVE STOPPED ACFT AT FIRST SIGN OF DISTR/CONFUSION AND RESOLVED ISSUES.