ZHU CONTROLLER DESCRIBED TCAS RA EVENT THAT RESULTED FROM AN AIRCRAFT FAILING TO MEET ANTICIPATED CLIMB RATES AND AN AIRCRAFT WHO WAS ON THE WRONG FREQUENCY.

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IN THE HOU SECTOR; ZHU; ACR X; CLBING OUT OF AUSTIN DIRECT LFK. WAS OVER TNV CLBING FL299/FL350 WAS ASKED IF HE COULD BE LEVEL IN 4 MINS; SAID YES. OPPOSITE DIRECTION OVER LFK WAS ACR Y LEVEL FL340. HAD APPROX 6 MINS BEFORE LOSS OF SEPARATION. SEVERE WX IN THE AREA WITH PASSING OF A COLD FRONT. SECTORS ON EITHER SIDE WERE HOLDING ACFT WITH MULTIPLE ACFT DIVERTING TO ALTERNATE ARPTS. SECTOR WAS EXTREMELY BUSY WITH DEVIATING ACFT AND DIVERTING ACFT. FREQ CONGESTION WAS A PROB. BOTH R- AND D-SIDE WERE STAFFED. TRACKER POS PROBABLY SHOULD HAVE BEEN STAFFED. NOT SURE IF STAFFING WAS AVAILABLE FOR THAT. REALIZED ACR X WAS NOT GOING TO TOP ACR Y; ATTEMPTED TO DSND ACR Y TO FL330. ACR Y WAS NOT ON FREQ. WITH ALL THE WX AND ACR Y WAS NEVER SWITCHED TO OUR FREQ AND WE DID NOT REALIZE THIS UNTIL WE ATTEMPTED TO DSND HIM. WITH APPROX 30 MI HEAD-ON; ACR X CLBING OUT OF FL339; 4 MINS LATER AND STILL NOT LEVEL; ACR Y RPTED ON THE ADJACENT SECTOR (IZD) RESPONDING TO AN RA AND DSNDING TO FL330. IZD SECTOR WAS EXTREMELY BUSY HOLDING APPROX 10-15 ACFT. IZD CTLR DID NOT KNOW WHO ACR Y WAS SINCE HE WAS NOT IN HIS SECTOR; BUT WAS EXTREMELY WORRIED BECAUSE HE HAD ACFT DSNDING AND HE THOUGHT IT COULD BE IN HIS HOLDING STACK. WHILE THIS WAS GOING ON; THE HOU D-SIDE CALLED ZFW PAXTO SECTOR TO ATTEMPT TO HAVE ACR Y DSNDED TO FL330. RADAR CTLR TURNED ACR X 30 DEGS L AND EXPEDITED HIS CLB. ACR X WENT FROM PROBABLY 500 FPM TO 700 FPM AND TOOK HIS TIME TURNING. THIS DID NOT HELP THE SITUATION AT ALL. NEITHER DID HE COME CLOSE TO BEING LEVEL IN 4 MINS. HE ALSO DID NOT EXPEDITE HIS CLB OR TURN. HAD ANOTHER ACFT SAME RTE AS ACR X TNV DIRECT LFK AT FL330 30 MI IN TRAIL OFF ACR X. ACR Y DATA BLOCK SHOWED DSNDING TO FL330 WHICH PUT HIM NOW HEAD-ON WITH SECOND ACFT. CLBED SECOND ACFT TO FL340 NOT KNOWING THAT ACR Y WAS RESPONDING TO RA AND WOULD BE CLBING BACK TO FL340. WE WERE THINKING D-SIDE GOT A HOLD OF PAXTO SECTOR AND THEY DSNDED THE ACR Y. ACR Y NOW SHOWED CLBING BACK TO FL340 HEAD-ON WITH SECOND ACFT. AT FL340; TURN SECOND ACFT 90 DEGS R. BY NOW ACR Y HAD CHKED ON THE IZD SECTOR FREQ AND WAS IMMEDIATELY DSNDED BACK DOWN TO FL330 AND TURN 40 DEGS R. PLT EXTREMELY UPSET BY EVERYTHING THAT WAS GOING ON. CAN'T SAY I BLAME HIM. THIS WAS ALL GOING ON WHILE STILL WORKING 15-20 OTHER ACFT. THERE WAS NO LOSS OF SEPARATION BTWN ANY ACFT AT ANY TIME. ALL ACFT WERE EVENTUALLY CLRED BACK ON COURSE. ACR X RPTED LEVEL APPROX 7 MINS AFTER ASKED. TRACKER POS WAS THEN STAFFED WHILE WE CONTINUED TO WORK THROUGH THE PROB AND WX. 2 MAIN FACTORS: ACR Y NEVER SWITCHED TO RIGHT FREQ BECAUSE OF RERTES AND WX; AND THE CTLR TRUSTING PLT TO COMPLY WITH WHAT HE SAID. IN HINDSIGHT; NO RESTR WAS GIVEN TO ACR X TO BE LEVEL AND PROBABLY SHOULD HAVE BEEN. CTLR THOUGHT HE HAD PLENTY OF TIME AND IF HE DIDN'T; HE COULD JUST DSND THE ACR Y SINCE HE WAS LNDG SOON ANYWAY. IN THE CTLR'S JUDGEMENT; IT WOULD BE BETTER TO HAVE ACR X AT ALT WHEN HE HAD A CHANCE TO; RATHER THAN TRYING TO CLB HIM LATER WITH EVEN MORE TFC TO HAVE TO CONSIDER. ALSO; THE INACTION OF THE ACR X PLT TO CLB OR TURN IN A TIMELY MANNER FURTHER COMPLICATED THE SITUATION.