POTENTIAL CONFLICT ENSUES BECAUSE OF AN ACFT EQUIP PROB VOR MALFUNCTION. HDG TRACK POS DEV.

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WE DEPARTED LOUISVILLE; KY; ON A PART 91 FLT TO COLUMBUS; NE. ATC CLRNC READ DERBY CITY 1 DEP; V4 TO APOLO INTXN; 5000 FT AND RWY HDG. WE TOOK OFF RWY 01 AND DEP ASSIGNED I BELIEVE A HDG OF 310 DEGS. WE WERE FLYING 310 DEG HDG WHEN DEP CTL ASSIGNED US TO TURN L TO 230 DEG HDG CLB 10000 FT AND INTERCEPT V4 TO APOLO INTXN. WE PROCEEDED WITH THE CLRNC TO 230 DEG HDG. THE CDI NEEDLE WAS SET ON COURSE AND BEGAN TO INDICATE THE COURSE WAS COMING ALIVE. I TURNED THE AIRPLANE BACK TO THE R TO STAY ON THE ASSIGNED COURSE. THE CDI NEEDLE SEEMED TO KEEP MOVING TO THE R. I TURNED THE AIRPLANE ACCORDING TO THE NEEDLE INDICATION. A FEW MOMENTS LATER WE NOTICED A DIFFERENCE BTWN #1 AND #2 CDI NEEDLES WHICH WERE SET ON THE SAME COURSE OFF OF THE LOUISVILLE VOR. THE #2 NAV INDICATED WE WERE N OF COURSE AND #1 NAV INDICATED WE WERE S OF COURSE. WE DOUBLE CHKED VOR FREQS AND IDENTED THEM. THERE WAS A DIFFERENCE THAT WE VERIFIED BY THIS TIME SO WE DOUBLE CHKED WITH THE GPS. IT SHOWED WE WERE N OF COURSE 15 MI. AT THIS TIME THE GPS INDICATED TO TURN TO APOLO INTXN TO THE S. THIS TURN REQUIRED A 90 DEG TURN TO THE L. WE THEN TURNED THE AIRPLANE TO APOLO INTXN. SOON AFTER WE RECEIVED A BROKEN XMISSION FROM ATC TO TURN 30 DEGS TO THE R. WE TRIED TO CHK ABOUT 4 OR 5 TIMES WITH ATC ABOUT THE NEW HDG BUT GOT NO RESPONSE. AFTER WE PASSED APOLO WE PROCEEDED TO OUR DEST OF COLUMBUS; NE. WE TRIED A FEW MORE TIMES TO CONTACT ATC ABOUT THE 30 DEG TURN HE ASSIGNED. HE THEN REPLIED 'DISREGARD.' WE THEN CONTINUED TO DEST. THE APPARENT PROB WITH OUR TURN BACK TO APOLO INTXN AFTER WE DISCOVERED WE WERE N OF COURSE IS WE PENETRATED THE SPACING OF ANOTHER ACFT. THAT IS THE PROB AT HAND. BUT NOTHING WAS EVER SAID TO US AFTER THE INCIDENT HAPPENED. I BELIEVE WE SHOULD HAVE BEEN NOTIFIED OF THE PROB SINCE IT WAS A SEVERE PROB. IT WASN'T BROUGHT TO MY ATTN UNTIL THE NEXT DAY BY MY CHIEF PLT OF THE COMPANY I AM CURRENTLY EMPLOYED. I BELIEVE WE DID OUR PART TO TRY TO TROUBLESHOOT THE NAV PROB. I KNOW THIS INCIDENT WOULD NOT HAVE HAPPENED IF THE NAV #1 WAS INDICATING PROPERLY. ALSO THE CTLR SHOULD HAVE CAUGHT THAT WE WERE OFF COURSE AND INQUIRED.