TWR ACR ACFT IN CLOSE PROX AT SAME ASSIGNED ALT. CLOSE TO OPERATIONAL ERROR WITH POTENTIAL FOR NMAC.

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OUR FLT X WAS IFR FROM BUF TO CLE; AND HAD BEEN SLOWED TO 250 KTS AND DSNDED TO 10000'. THE LAST SEGMENT OF THE ENRTE PORTION OF THE FLT WAS TO PROCEED DIRECTLY TO CHARDON VOR THEN THE 246 DEG R TO NOELS INTXN; THEN WE WOULD NORMALLY BE HANDED OFF TO CLE APCH FOR A VECTOR TO A FINAL APCH FIX. AS WE APCHED NOELS INTXN; THE CLE ARTCC CTLR TOLD US TO CONTACT CLE APCH CTL. UPON CONTACTING THEM; THEY TOLD US TO RETURN TO OUR PREVIOUSLY ASSIGNED FREQ (CLE ARTCC); WHICH WE DID. CLE ARTCC THEN TOLD US TO CONTACT CLE APCH; WHICH WE DID AGAIN; WITH THE SAME RESULTS. (RETURN TO PREVIOUS FREQS). AT THIS POINT; WE WERE OVER NOELS INTXN; STILL UNDER CTL OF CLE ARTCC SO IT TOLD THEM THAT WE WERE STILL UNABLE TO STAY WITH CLE APCH AND THAT WE WERE GOING TO HOLD AT NOELS INTXN AT 10000'. THE CTLR (ARTCC) GAVE HER APPROVAL. AS WE STARTED THE RIGHT TURN; SHE CAME BACK ON FREQ; AND SAID; 'MAKE AN IMMEDIATE LEFT TURN AND DSND TO 9000';' WHICH WE DID. AT THE SAME TIME; SHE ALSO TOLD ACR Y TO MAKE AN IMMEDIATE RIGHT TURN. AT THIS POINT WE SAW THE OTHER ACFT; AT ABOUT 4-5 MI DISTANCE. AFTER THE TURN AND DSCNT AND A HDOF TO CLE APCH WAS MADE WITH A VECTOR AND APCH. (AT THIS TIME; CLE HAD OVCST SKIES AND WERE DOING ILS APCHS). AFTER REACHING THE GATE; I CALLED THE APCH CTL SUPVR TO FIND OUT WHAT HAD HAPPENED. HE TOLD ME THAT THERE HAD BEEN A COMPUTER GLINCH; AND THAT THEY HAD NEVER GOTTEN OUR COMPUTER TAG. I THEN CALLED CLE CENTER SUPVR AND THEIR PERSON IN CHARGE OF QUALITY ASSURANCE; AND WAS TOLD ALSO THAT THERE WAS A PROB WITH THE COMPUTER; AND THAT THEY WERE INVESTIGATING. THE NEXT DAY; CLE CENTER SUPVR CALLED ME AT HOME AND SAID THAT THE PROB WAS WITH THE COMPUTER DROPPING OUR RADAR TAG; AND ACQUIRING SOMEONE ELSE'S WITH A DIFFERENT TRANSPONDER CODE. CLE CENTER ALSO SAID THAT APCH HAD TAKEN OUR HDOF; BUT APCH SAID THEY NEVER RECEIVED IT. THE SUPVR SAID THAT THEY WOULD CONTINUE TO FIND THE COMPUTER PROB; BUT THAT THEY WOULD PURSUE NO OTHER ACTION. THEY ALSO SAID THAT THE CENTER'S ALERT (SNITCH) DIDN'T GO OFF. PS: WHEN WE WERE ON APCH'S FREQ; WE DID HEAR ANOTHER FLT THAT HAD SOMEONE ELSE'S TRANSPONDER CODE. SUPPLEMENTAL INFO FROM ACN 94760: WE (ACR Y) WERE ON VECTORS FOR CLE ARR. CLE CENTER WAS WORKING US. THEY HAD ALREADY GIVEN US NUMEROUS OFF ARWY TURNS AND HAD OUR SPD REDUCED TO 250 KTS FOR SPACING DUE TO TFC CONGESTION. THE CTLR WAS VERY BUSY AND WAS PROBABLY AT A MAX TFC LOAD. ACR X CAME BACK ON OUR FREQ AND STATED APCH SENT HIM BACK TO CENTER FREQ BECAUSE HE HAD NO INFO ON HIM. THE CTLR TOLD HIM TO TURN RIGHT IMMEDIATELY AND DSND IMMEDIATELY TO 9000'. (I COULD HEAR THE PANIC IN THE CTLR'S VOICE). WE WERE THEN TOLD TO 'TURN RIGHT IMMEDIATELY VERY TIGHT TURN.' I DISENGAGED THE AUTOPLT AND BRISKLY ROLLED INTO A 45 DEG R BANK. WE WERE NEVER TOLD WHERE TO LOOK FOR TFC OR HOW CLOSE IT WAS. THE CONFLICTING TFC RPTED US IN SIGHT SHORTLY AFTER OUR TURN WAS INITIATED. WE NEVER DID SEE HIM. I HOPE IT DOESN'T TAKE A MAJOR DISASTER FOR CONGRESS TO LET GO OF THE AVIATION TRUST FUND PURSE STRINGS!