ACR X HAD LTSS FROM ACR Y. SYS ERROR. ACR X AND Y WX AVOIDANCE.

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I WAS WORKING THE RADAR POS AT SECTOR 29; A HIGH ALT SECTOR AT ZKC. THERE WAS A MANUAL PERSON AND A TRACKER ALSO AT THE POS. THERE WAS A LINE OF HVY WX EXTENDING FROM N OF CHICAGO DOWN INTO TEXAS. EVERY ACFT ON FREQ WAS DEVIATING AND MOST WERE GOING THROUGH 1 HOLE IN THE WX NEAR DGD VOR. ACR X HAD BEEN RERTED INTO MY SECTOR AND WAS WBOUND; DEVIATING S OF COURSE; WHEN HE CHKED ON. ACR X WAS AT FL350 REQUESTING FL390. THERE WAS OPPOSITE DIRECTION TFC AT FL390 AT THAT TIME SO ACR X WAS CLRED TO FL370 AND TOLD TO EXPECT FL390 WHEN CLR OF TFC. ACR Y WAS AT FL370 SEBOUND WHEN HE CHKED ON DEVIATING S FOR WX. THERE WAS A LOT OF CONGESTION IN THAT AREA. IT WAS THEN I REALIZED THE POSSIBLE CONFLICTION BUT AT THAT POINT I DIDN'T THINK SEPARATION WOULD BE COST. BOTH ACFT WERE IN THE MIDDLE OF THE WX SO I ASKED ACR X IF HE COULD TURN 30 DEG R FOR TFC. HE SAID NOT FOR ABOUT 20 MI. I TOLD ACR S TO TURN 30 DEG R AS SOON AS HE COULD FOR TFC AND CLBED HIM TO FL390 AND TO EXPEDITE. I ASKED ACR Y IF HE COULD TURN R FOR TFC. HE SAID IN A MIN OR 2. I TOLD ACR Y TO TURN 30 DEG R FOR TFC. I ASKED ACR X IF HE WAS TURNING YET AND HE ASKED IF I COULD WAIT 10 MORE MI. I SAID NEGATIVE AND TO TURN 30 DEG R FOR TFC. I ASKED ACR Y IF HE WAS TURNING YET. HE SAID HE WAS STARTING THE TURN RIGHT NOW. I TOLD ACR Y TO TURN 50 DEG R FOR TFC. HE ROGERED. AT THAT TIME I OBSERVED WHAT APPEARED TO BE LESS THAN 5 NM SEPARATION BTWN ACR X AND ACR Y. I FEEL SOME OF THE CONTRIBUTING FACTORS WERE; THE WX OF COURSE. ALSO THE HISTORY'S ON THE RADAR WERE TURNED TO '0' AS PER THE AREA MGRS REQUEST. THIS WAS BECAUSE THE COMPUTER WAS REACHING ITS OVERLOAD CAPACITY. I ALSO FEEL THE TFC MGMNT UNIT DID VERY LITTLE TO HELP. THE AREA SUPVR HAD REQUESTED TMU HELP BY REROUTING SOME ACFT OUT OF THE AREA. THIS REQUEST WAS MADE SEVERAL TIMES BUT I DON'T BELIEVE ANYTHING WAS DONE UNTIL AFTER THE OPERROR. ALL EVENING; A GREAT DEAL OF E-W TFC WAS RERTED TOWARD THAT HOLE NEAR DGD. I BELIEVE IT HAS BEEN DETERMINED SO FAR THAT THE CLOSEST POINT WAS 4.5 NM AND 100 FT.