A CGA HS25 JET DEPARTED BDR AND PROCEEDING DIRECT ELIOT INTXN DISCOVERED THAT THEIR NAV SYS WAS NOT WORKING PROPERLY AND INFORMED ATC. THE APCH CTLR ISSUED A REVISED CLRNC. IT APPEARS THAT THE ACFT WAS OFF COURSE AND CONFLICTED WITH AN ACR RESULTING IN LTSS.

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WE DEPARTED BDR TO AOH. OUR CLRNC WAS THE BRIDGEHAVEN 5 DEP DIRECT ELIOT INTXN; THEN DIRECT ETX. WE DEPARTED BDR AND RECEIVED SEVERAL RADAR VECTORS AND STEP UPS TO 15000 FT MSL OVER THE NEXT APPROX 10 MINS. OUR ACFT; A HAWKER 125-600; IS EQUIPPED WITH A GLOBAL VLF OMEGA FOR LONG RANGE NAV. APPROX 10 MINS AFTER DEP; NEW YORK DEP TOLD US TO 'PROCEED DIRECT ELIOT.' WE NEVER RECEIVED AN INITIAL HEADING TO ELIOT. WE ENTERED DIRECT ELIOT AND TURNED TO THAT HEADING. AFTER WE WERE DIRECT WE BEGAN TO VERIFY OUR POS AND DISCOVERED THE DISTANCE AND BEARING WAS INCORRECT. WE THEN IMMEDIATELY INFORMED DEP THAT OUR LONG RANGE NAV WAS NOT WORKING PROPERLY AND WE WERE CHANGING OUR EQUIP SUFFIX FROM A /R TO A /A AND REQUESTED DIRECT EAST TEXAS VOR. THE CTLR THEN GAVE US A RADAR VECTOR TO INTERCEPT THE 252 DEG RADIAL OF SAX; THEN TO ELIOT AND DIRECT EAST TEXAS. WE INFORMED HIM THAT WE WOULD TRY AND RE-INITIALIZE THE OMEGA OVER EAST TEXAS. THERE WAS NO TFC RPTS OR ALERTS GIVEN DURING THIS TIME; NOR WAS ANY EVASIVE ACTION TAKEN BY EITHER ACFT. WE CONTINUED ON TO OUR DEST AS NORMAL. IT WAS NOT UNTIL 2 DAYS LATER THAT WE LEARNED THERE HAD BEEN AN ACFT NEAR US AT THAT TIME. WHEN WE DISCOVERED THE OMEGA WAS INCORRECT INFORMING ATC BECAME OUR FIRST PRIORITY. IF A TFC PROB WAS DEVELOPING IT SHOULD HAVE BECOME THE CTLR'S TOP PRIORITY TO INFORM US OF THE TFC OR WRONG BEARING TO ELIOT OR ASSIGNED US A NEW HEADING OR VECTOR.