RWY EXCURSION - FLC FAILED TO HOLD SHORT OF THE RWY (IE; SHORT OF THE 'HOLD SHORT' LINE).

Narrative

LGA - LNDG RWY 31 DEP; RWY 4; STANDARD FOR WX AND WIND AT THE TIME. I WAS PIC IN A DA-50 POSITIONING TO PICK UP 3 PAX TO TAKE THEM TO SKBO (BOGOTA; COLUMBIA) WE HAD A MECH IN THE JUMPSEAT WHICH IS SOP FOR OUR INTL/OPS - NO PAX. AFTER LNDG WE WERE ASKED BY TWR IF WE COULD TURN OFF AT THE HIGH SPD TXWY (THAT JOINED 'O') WE SAID WE COULD (AGAIN STANDARD ROLL OUT OF OUR ACFT USING THAT RWY) BOTH PLTS (SENIOR PLTS) HAVE SIGNIFICANT EXPERIENCE IN DA-50 AND LGA OPS. AS WE TURNED OFF RWY WE WERE TOLD TO CALL GND CTL. I DID; OUR TAXI INSTRUCTIONS WERE - 'OUTER - FOX - HOLD SHORT OF RWY 4.' THIS WAS A STANDARD CLRNC BOTH CREWMEMBERS WOULD EXPECT. I READ BACK TAXI CLRNC INCLUDING; 'HOLD SHORT OF RWY 4.' AS I READ THE CLRNC BACK I LOOKED TOWARD THE PLT TO MAKE SURE HE HAD HEARD THE XMISSION. HIS NODDING GESTURE INDICATED TO ME THAT HE HEARD IT - I DO NOT SPECIFICALLY REMEMBER IF HE VERBALLY REPEATED 'SHORT OF RWY 4.' I WAS CONVINCED EVERYONE WAS CLR AS TO TAXI INSTRUCTIONS. I WAS ASKED TO DO THE AFTER LNDG CHKLIST; WHICH I INITIATED SHORTLY AFTER TAXI CLRNC WAS RECEIVED. AS WE WERE TAXIING I ANNOUNCED THAT I WAS STARTING THE APU; (STANDARD PROC FOR THIS TYPE OF TURN AROUND). AS I INITIATED THE START ON THE APU -- OUR EFIS TUBES SHOWED ERROR MESSAGES AND THE TUBE WENT BLACK MOMENTARILY; THIS IS ABNORMAL FOR AN APU START IN THIS CONFIGN. I WAS MONITORING THE START AS WELL AS THE PROB; WHICH APPEARED TO BE A MOMENTARY PWR SURGE. OUR MECH WAS ALSO MONITORING THE START AS WELL SINCE BOTH PLTS INDICATED THAT THERE WAS A PROB. WHEN I LOOKED UP FROM THE APU PANEL I SAW RWY 4 APCHING AND TOLD THE PLT TAXIING THE ACFT TO STOP -- AT THE SAME TIME GND CTLR CAME ON FREQ AND SAID; 'HOLD; HOLD; HOLD.' THE ACFT WAS MOVING VERY SLOWLY DURING OUR TAXI.I ANNOUNCED TO GND CTL THAT WE WERE HOLDING SHORT OF RWY 4 AND WE WERE STOPPED. OUR ACFT HAD PASSED THE HOLD LINE WHICH WAS NOW BELOW THE WING; THE ACFT WAS WELL SHORT OF THE RWY. THE TWR HAD JUST CLRED AN ACR FOR TKOF AS WE APCHED THE HOLD LINE FOR RWY 4 AT FOX. THE TWR CANCELED THE TKOF CLRNC SHORTLY AFTER THE ACR STARTED HIS TKOF ROLL. THE PLT TAXIING SAID HE WAS AWARE OF THE NEED TO HOLD SHORT BUT WAS MONITORING OUR PROB AS WAS I AND THE MECH. CLASSIC NO ONE WATCHING THE STORE.