ZID CTLR DESCRIBED NEAR OPERROR AT FL380 WHEN CONFLICTING TFC WAS NORDO AND COORD WITH ADJACENT SECTOR WAS HURRIED.

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ACFT X WAS GIVEN DIRECT PSK FROM ZOB. I CALLED ZOB C69 AND TOLD THEM I COULD NOT TAKE THAT FLT AT FL380 BECAUSE OF TFC ON J149 DEPARTING OUT ZDC. (THEY REPLIED I ONLY SEE LIMITEDS.) I TOLD THEM ACFT X NEEDS TO BACK E. ZOB THEN ASKED IF I WOULD TAKE ACFT X AT FL370 WADOF. I SAID IF ZDC (W42) WOULD APPROVE IT I WOULD ACCEPT THE FLT AT FL370 (BY GIVING ACFT X DIRECT PSK THE ACFT FLIES 2 MI INTO MY AIRSPACE INTO ZDC. ACFT X DATA BLOCK REAPPEARED WITH FL370 IN THE DATA BLOCK (SHOWING FL380 DSNDING TO FL370). WE THEN TOOK HDOF ON ACFT Y ON J149 WBOUND AT FL380. AS OF THIS TIME ACFT X HAD NOT STARTED A DSCNT. WHEN ACFT WERE 15 NM APART CONVERGING AT 90 DEGS L ZOB CALLED AND SAID ACFT X WAS NORDO AND DID NOT GET THE DSCNT. AT THE SAME TIME ZID (W42) WAS CALLING EMER ON LANDLINES TO TELL US THEY HAD SHIPPED ACFT Y TO US AND ZOB SAID ACR X WAS NORDO. I THEN HUNG UP AND TRIED ACFT X TO SEE IF THE ACFT WAS ON OUR FREQ (NO LUCK). ACFT Y HAD JUST CHKED IN PRIOR TO THAT AND WAS THEN GIVEN A TA AND TOLD TO DSND. ACFT Y LEVELED AT FL370 WHEN ACFT X WAS APPROX 5.1 NM N OF HIM.