ACR X HAD NMAC LTSS FROM SMT Y. EVASIVE ACTION CLB. SYS ERROR.

Narrative

SMT Y DEPARTED MID CONTINENT ARPT (ICT) RWY 19L INTO IMC. ACR X WAS CLRED INTO POS AND HOLD RWY 19L APPROX 30 SECONDS TO 1 MIN LATER. AFTER TAXIING INTO POS AND HOLDING (WHICH MAY HAVE TAKEN ANOTHER 30 SECONDS); ACR X WAS CLRED FOR TKOF TO 'FLY RWY HDG.' OUR INITIAL CLRNC ALT WAS 5000 FT MSL. ONCE AIRBORNE; AT POSSIBLY 2000 FT MSL; WE WERE TOLD TO TURN R HDG 210 DEGS. WE WERE THEN ASKED TO CONTACT DEP CTL. I WAS THE PF AND MY FO SWITCHED TO DEP AND INITIATED A CALL TO DEP CTL. THIS MET WITH NO RESPONSE FROM DEP. AGAIN; AFTER A SHORT TIME MY FO CALLED AND RPTED ON FREQ THAT WE WERE ON HIS FREQ OUT OF (APPROX 4200 OR 4300 FT) CLBING TO 5000 FT). CTLR ACKNOWLEDGED THIS. SHORTLY AFTER THIS; THE SMT Y THAT HAD DEPARTED AHEAD OF US EMERGED FROM MY L JUST SLIGHTLY BENEATH US AT OUR APPROX 10 O'CLOCK OR SO POS AND I ASSUME WAS ALSO IN A CLB. I IMMEDIATELY PULLED UP AND MY FO RPTED THIS TO DEP (THAT WE'D JUST MISSED THE SMT). DEP GAVE US AN IMMEDIATE TURN (TOO LATE BY THEN) TO 100 DEGS. TONE OF HIS VOICE WAS OBVIOUSLY STRAINED. A DIFFERENT VOICE DIRECTED US ON COURSE. HARD TO JUDGE DISTANCE; BUT REALLY CLOSE IF YOU CAN SEE ANOTHER PLANE IMC.