A NORDO PA32 COORDINATED WITH TRACON SUPVR FOR DEP FROM ARPT WITHOUT RADIOS AND WAS APPROVED AND GIVEN A WBOUND DEP TO FOLLOW. CTLR TRAINING IN PROGRESS IN TRACON WITH COMBINED POS CONFIGN. APCH CTLR AND TRAINEE SAW PA32 DEPART NW VERSUS WE AND TOWARDS A CL65 ON THE ILS FOR RWY 11. TRAINEE AND APCH CTLR UNABLE TO CONTACT CL65 TO TURN HIM AND WATCHED AS THE ACFT PASSED IN CLOSE PROX.

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I WAS CONDUCTING OJT ON RADAR N; ALL RADAR POS COMBINED. MODERATE TFC; SCATTERED WX IN THE AREA. A PLT CALLED THE TRACON AND TALKED TO OUR SUPVR. THE PLT SAID HE WAS IN HIS PLANE (A PA32); AT CAE; WITHOUT WORKING RADIOS; AND WANTED TO DEPART RWY 23; WBOUND; TO A DEST 'JUST N OF IRQ VOR.' SUPVR APPROVED IT; GAVE THE PLT A CODE TO SQUAWK; TOLD ME ABOUT IT. THE AIRPLANE DEPARTED; SQUAWKING 7600; AND TURNED NW; CLBING DIRECTLY TOWARD AN ACR CL65 WHICH THE DEVELOPMENTAL HAD JUST TURNED ON THE ILS APCH FOR RWY 11. THE DEVELOPMENTAL ATTEMPTED TO BREAK THE CL65 OUT; BUT GOT NO RESPONSE. I ALSO TRIED TO CAL THE CL65. JUST AS THE ACFT PASSED; LCL CTLR CALLED AND SAID THE CL65 WAS ON HIS FREQ. AFTER LNDG; THE CL65 CALLED UP ON APCH FREQ AND APOLOGIZED FOR SWITCHING TO TWR EARLY; AND SAID THEY HAD THE OTHER ACFT IN SIGHT. THE NORDO ACFT CONTINUED NW FOR ABOUT 15 MI; THEN TURNED WBOUND. HE DEPARTED OUR AIRSPACE TO THE W; CLBING THROUGH 8000 FT; STILL SQUAWKING 7600. WE ADVISED THE NEXT FACILITY; AGS.