ZJX CTLR EXPERIENCED CONFLICT AT 8000 FT WHEN UNKNOWN IFR TFC CONFLICTED WITH ANOTHER IFR ACFT DEVIATING AROUND WX.

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I WAS WORKING R12/R13. I WAS ON POS FOR ABOUT 1 HR WORKING MODERATE LEVEL TFC BY MYSELF. I HAD MULTIPLE PRACTICE APCHS; DEPS; ARRS; AND MIL OPS. TSTMS AND TOWERING CUMULUS WERE BUILDING RAPIDLY. I ACCEPTED A HDOF FROM T21 ON ACFT Y; A KING AIR INBOUND TO ABY. HE CHKED ON WITH ATIS INFO AT 11000 FT. I ISSUED THE ALTIMETER AND INSTRUCTED TO EXPECT A VISUAL APCH TO RWY 4. A FEW MINS LATER; WHEN ACFT X ENTERED MY AIRSPACE; HE REQUESTED LOWER. I ISSUED A DSCNT TO 7000 FT; FOR AN OVERFLT NWBOUND AT 6000 FT. ACFT Y WAS OBSERVED OUT OF 9000 FT AND SELF-INITIATED A TURN TO THE SW. I ASKED THE PLT IF HE WAS DEVIATING AND AT THE SAME TIME NOTICED A LIMITED DATA BLOCK AT 8000 FT NWBOUND. CONFLICT ALERT INITIATED BTWN ACFT X AND THE LIMITED AT 8000 FT. I ISSUED THE TFC CALL AND ACFT X STATED THAT HE WAS DEVIATING FOR A BUILDUP AND WAS TURNING BACK TO ABY. BEFORE ACFT X STARTED HIS TURN BACK; HE WAS AT 8000 FT DSNDING TO 7000 FT AND WAS WITHIN 1 1/2 MI OF THE 8000 FT LIMITED. I DID NOT THINK TWICE ABOUT THE 8000 FT LIMITED BECAUSE VFR ACFT DURING WX TYPICALLY FLY AT IFR ALTS TO AVOID CLOUDS. ONCE ACFT X CLRED THE 6000 FT TFC; I DSNDED HIM TO 3000 FT AND TOLD HIM TO RPT THE ARPT IN SIGHT. HE RPTED THE ARPT IN SIGHT AND I CLRED HIM FOR THE VISUAL APCH TO RWY 4 AND SWITCHED HIM TO THE TWR FREQ. CSG APCH THEN CALLED ME AND ASKED IF I WAS WORKING ACFT Z. I DID NOT KNOW THE ACFT. THE APCH CTLR THEN SAID HE WAS AT 8000 FT; 20 MI SE OF EUF. I NOTICED THE CODE; WHICH WAS THE 8000 FT TFC; AND ENTERED THE CODE INTO THE COMPUTER TO GET A FLT PLAN READOUT. THE COMPUTER SHOWED THE ACFT TO BE AN ACFT Z PA32 DEPARTED BKV NBOUND ON V35 FROM CTY TO PZD; THEN V321 TO CSG. THEN I TOLD THE APCH CTLR THAT I SEE THE FLT PLAN BUT I DID NOT WORK THE ACFT OR EVER RECEIVE A HDOF ON HIM. THE CODE WAS ALSO STILL UNCORRELATED IN OUR SYS; SO OUR COMPUTER WAS NOT TRACKING HIM. AT THIS TIME THE ACFT WAS STILL IN MY AIRSPACE AND THEN SHOWED UP ON MY URET DISPLAY AS BEING OVERDUE. THE CSG APCH CTLR SAID THAT HE IS TALKING TO THE ACFT AND IS WORKING HIM NOW. I IMMEDIATELY CALLED MY SUPVR AND TOLD HIM ABOUT THE SITUATION. I WAS UP FOR BREAK; SO I WAS RELIEVED. THE SUPVR ASKED ME QUESTIONS ABOUT THE AIRSPACE AND THEN CALLED TLH APCH; WHICH WOULD HAVE WORKED THE ACFT. TLH APCH SAID THAT THEY FLASHED THE DATA BLOCK TO VLD APCH AND THEN THEY FLASHED IT BACK TO TLH APCH. I DID NOT NOTICE THE LIMITED DATA BLOCK GOING THROUGH MY AIRSPACE AS AN IFR BECAUSE WE TYPICALLY SEE VFR'S AT IFR ALTS AND ON WRONG CODES. ALSO DUE TO THE COMPLEXITY OF TFC AND WX I DID NOT HAVE TIME TO INVESTIGATE THE CODE IF I WOULD HAVE SEEN IT. MGMNT IS STILL INVESTIGATING WHERE THE BREAKDOWN WAS ENCOUNTERED. THE INCREASING LEVEL OF TFC; LACK OF QUALIFIED CTLRS; TIME ON POS; FATIGUE; WX AND PLTDEV OF WX WERE ALL CONTRIBUTING FACTORS TO THIS EVENT.