ACFT AT WRONG ALT FOR DIRECTION OF FLT RECEIVED A TA COMMAND FROM TCASII.

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UNABLE TO CONTACT ZOB AFTER A HDOF FROM ZID; WE WERE LEFT FLYING LEVEL AT OUR LAST ASSIGNED ALT (FL280); HEADING EBOUND ON AN ASSIGNED HEADING OF 55 DEGS. (THE WRONG ALT FOR THAT DIRECTION.) SUDDENLY OUR COLLISION AVOIDANCE SYS ALERTED US TO HEAD-ON TFC AT THE SAME ALT. WE HAD TO RADICALLY DEVIATE FROM OUR ALT TO AVOID A WBOUND CITATION. THE RADAR WENT OUT AT INDIANAPOLIS WHILE WE WERE CLBING OUT FROM CVG. WE WERE BEING STEPPED UP TO FL290 WITH SEVERAL LEVEL INTERMEDIATE LEVEL OFFS. ZID BECAME VERY BUSY BUT SOON WE WERE TOLD TO CALL ZOB; I WAS GLAD TO BE BACK IN A RADAR ENVIRONMENT. I RPTED TO CLEVELAND THAT WE WERE LEVEL AT FL280 ON 55 DEGS ASSIGNED. BUT THE CTLR WAS SO BUSY PUTTING OTHER ACFT IN HOLDING PATTERNS TO KEEP THEM OUT OF INDIANAPOLIS' AIRSPACE THAT HE DID NOT RESPOND TO US. HE SAID; 'EVERYONE STANDBY; DON'T CALL ME I'LL CALL YOU.' WE WERE JUST PASSING CTW AT THIS TIME. WE WERE LISTENING; HOPING TO CHK IN SOON BUT NOT WANTING TO INTERRUPT HIM; WE WAITED. THOSE WHO TRIED TO CONTACT HIM WERE TOLD TO STANDBY OR LEFT UNANSWERED. ALL OF A SUDDEN OUR BFG SKYWATCH CALLED 'TFC.' IT WAS SHOWING A TARGET AT 12-1 O'CLOCK POS; AND 5 MI; 200 FT ABOVE US. (SKYWATCH UNITS ARE SLOW TO UPDATE THE INFO SO I THINK IT WAS CLOSER THAN THIS.) WE BEGAN AN IMMEDIATE DSCNT; PASSING ABOUT 1 OR 2 MI TO THE R OF THE OTHER ACFT WITH AN ALTIMETER READING OF 27300 FT. WE HAD VISUAL CONTACT WITH THE ACFT AT ABOUT 2 MI. AFTER PASSING THE OTHER ACFT WE WENT BACK TO OUR ASSIGNED ALT OF FL280 AND 55 DEGS HDG. IT TOOK 3 MORE CALLS TO GET A RESPONSE FROM CLEVELAND. AND THEN ALL THEY COULD DO WAS TO GIVE US ANOTHER FREQ. I FAILED TO REALIZE THAT INDIANAPOLIS'S HDOF WAS NOT A HDOF AT ALL BUT JUST A FREQ CHANGE. CLEVELAND DID NOT KNOW WE WERE COMING; THEY DIDN'T HAVE A COMPLETE STRIP ON US. HAD I KNOWN THIS I WOULD HAVE PUSHED THE CLEVELAND CTLR TO IDENT US OR CALLED ZNY TO GET A GOOD FREQ FOR CLEVELAND.