CORPORATE JET DEPARTING UNCONTROLLED ARPT INVOLVED IN NEAR COLLISION WITH A CHEROKEE COMMENCING TKOF ROLL ON AN INTERSECTING RWY.

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WE TAXIED FROM THE TERMINAL TO RWY 9 FOR DEP; CALLED UNICOM BEFORE TAXI TO ANNOUNCE AND WENT BACK TO CLRNC WHILE TAXIING TO CHANGE RWY FROM RWY 27 TO RWY 9. LCL TFC USING RWY 36 DUE TO WIND BUT WE WERE UNABLE DUE TO RWY LENGTH. CHANGED BACK TO UNICOM AT THE RWY; ACFT ON DOWNWIND FOR RWY 36 ANNOUNCED HE WOULD EXTEND TO LET US OUT. WE ACKNOWLEDGED; THANKED HIM; AND TOOK THE ACTIVE RWY WITH THE ANNOUNCEMENT WE WERE GOING TO START OUR ROLL. AT 5 KTS; BELOW V1 AND A FEW HUNDRED FT FROM THE INTXN OF RWY 36; A CHEROKEE CROSSED OUR PATH BEGINNING HIS DEP ROLL ON RWY 36. HE WAS GOING APPROX 25 KTS; AND WE NEVER HEARD HIM ANNOUNCE. THE PF STARTED TO PULL PWR FOR AN ABORT BUT WE BOTH DECIDED SIMULTANEOUSLY THAT WE WOULD MISS HIM AND I STATED; 'CONTINUE.' IT DID NOT APPEAR THE CHEROKEE EVER SAW US. I ATTEMPTED 1 RADIO CONTACT UNSUCCESSFULLY BEFORE SWITCHING TO DEP. THIS WAS THE CLOSEST CALL THE PF AND I HAVE EVER HAD IN OVER 30000 HRS OF TOTAL FLYING TIME. WE ESTIMATED WE WERE ABOUT 3-5 SECONDS FROM A DISASTER. WHEN WE FIRST SAW HIM XING FROM R TO L; HE WAS PROBABLY 200-300 FT FROM US. BY THE TIME WE PASSED BEHIND HIM; WE WERE PROBABLY 50 FT FROM HIM. I CALLED THE FBO THE NEXT DAY TO INQUIRE ABOUT THE INCIDENT AND SHE SAID SHE DID HEAR US RPTING ON FREQ THROUGHOUT; BUT DID NOT RECALL HEARING THE CHEROKEE; WHICH WAS FROM OUT OF STATE. WE THOUGHT WE MIGHT HAVE MISSED A CALL FROM HIM; OR THAT THE ACFT IN THE AIR WAS TALKING TO HIM INSTEAD OF US; BECAUSE I HAD SWITCHED BACK AND FORTH FROM CLRNC TO UNICOM. IN THE FUTURE; I WILL BE VERY CAREFUL TO MONITOR BOTH FREQS WHEN NECESSARY TO AVOID ANY POSSIBILITY OF MISSING A CRUCIAL CALL.