CL65 CREW HAD A RWY INCURSION AFTER TAXIING PAST THE TXWY THEY WERE INSTRUCTED TO HOLD AT.

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WE WERE CLRED TO TAXI INTO POS AND HOLD ON RWY 13 LGA. AS WE TURNED ONTO TXWY; A B737 BEHIND US RPTED THAT WE HAD AN ACCESS PANEL OPEN UNDER THE FO'S WINDOW ON THE NOSE. FO ADVISED TWR WE WOULD NEED TO RETURN TO THE GATE. TWR ADVISED US TO CONTINUE TO HOLD. I THEN TOLD THE FO TO ADVISE THE FLT ATTENDANT WHAT WAS HAPPENING AND WHY WE WOULD NOT BE TAKING OFF. WHILE THE FO WAS TALKING TO THE FLT ATTENDANT; TWR CALLED AND TOLD US TO TAXI; BUT HOLD SHORT OF TXWY AA. I READ BACK THE CLRNC INCLUDING THE HOLD SHORT OF TXWY AA. I COULD SEE NO TXWY SIGNS PRIOR TO THE INTXN OF RWY 4 AND ASSUMED (WRONGLY) THAT TXWY AA WAS ON THE OTHER SIDE OF RWY 4. I ALSO ASSUMED SINCE RWY 4 WAS ACTIVE FOR LNDG TFC AND TWR HAD NOT TOLD US TO HOLD SHORT OF RWY 4; THAT WE WERE CLRED TO CROSS IT. JUST AFTER XING RWY 4; TWR CALLED AND SAID 'SINCE YOU MISSED TXWY AA; TAKE THE NEXT R AND CONTACT GND.' AT THIS POINT I REALIZED MY MISTAKE AND APOLOGIZED TO TWR. HE SAID IT WAS OK; EVERYTHING WORKED OUT OK THIS TIME. WE CALLED GND; TAXIED BACK TO RAMP; GOT THE PANEL CLOSED; TAXIED BACK AND DEPARTED WITHOUT FURTHER INCIDENT. A FEW THINGS I FEEL COULD HAVE PREVENTED THIS INCLUDE: 1) I SHOULD HAVE HAD THE FO WAIT UNTIL CLR OF THE RWY TO TALK TO THE FA. 2) TWR SHOULD HAVE TOLD US TO HOLD SHORT RWY 4. THIS WOULD HAVE BEEN VERY CLR AS THE INTXN OF RWY 13 AND TXWY AA IS HARD TO SEE. AND OF COURSE; 3) HAD OUR GND CREW CLOSED THE PANEL AFTER UNPLUGGING THEIR HEADSET; NONE OF THIS WOULD HAVE HAPPENED.