B737-800 FLT CREW HAS A TCAS ALERT DURING CLB.

Narrative

DURING INITIAL CLB ON W9 FROM LA ROMANA; DOMINICAN REPUBLIC; WE AVERTED AN NMAC WITH A TWIN-ENG PROP DRIVEN ACFT. PRIOR TO DEP FROM MDLR OUR CLRNC WAS TO INTERCEPT W11 OUTBOUND TO PIXAR. WE DEPARTED OFF RWY 11 WITH A R TURNOUT AND CLRNC TO CROSS THE LRM VOR AT OR ABOVE 5000 FT. AFTER DEP AND JUST PRIOR TO XING OVERHEAD THE LRM VOR; SANTO DOMINGO DEP RECLRED US TO INTERCEPT W9 TO PTA AND TO CLB AND MAINTAIN 8000 FT. BOTH PLTS HAD THE LRM VOR FREQ SELECTED; SO I PROVIDED AN INITIAL INTERCEPT HDG TO W9 TO FO. AS THE PNF WITH MY SANTO DOMINGO 10-1 PAGE READILY AVAILABLE; I REPROGRAMMED THE FMC TO REFLECT OUR NEW CLRNC. WHILE CONTINUING OUR CLB AND AFTER ROLLING OUT AND INTERCEPTING W9 OUTBOUND FROM LRM; TCAS DISPLAYED AN ACFT 1100 FT ABOVE US ON A SOUTHWESTERLY HDG. THIS SUDDEN EMERGENCE OF AN ACFT ON MY MAP DISPLAY (10 MI RANGE; TCAS IN 'ABV' MODE) WITHIN 5 MI RAISED OUR SITUATIONAL AWARENESS. I SPOTTED THE ACFT VISUALLY AND QUICKLY DETERMINED THAT WE WERE ON A COLLISION COURSE. AT THIS TIME WE WERE CLBING THROUGH 7400 FT; WITH NO TCAS ADVISORY DISPLAYED OR AURAL ALERT AND THE TFC NOW DISPLAYED AT 700 FT ABOVE US. I INSTRUCTED FO TO STOP OUR CLB (7600 FT); THE APCHING ACFT WAS MAINTAINING ITS SOUTHWESTERLY HDG ON A DIRECT COLLISION COURSE. FO FOCUSED ON FLYING THE ACFT AND FOLLOWED MY INSTRUCTIONS WHILE I MAINTAINED VISUAL WITH THE APCHING ACFT. IN ORDER TO SEPARATE OURSELVES FROM THE ACFT WE HAD TO DSND. AFTER THE ACFT PASSED US; THE TCAS DISPLAYED THE ACFT 500 FT ABOVE US. I INFORMED SANTO DOMINGO DEP ABOUT THE NEAR MIDAIR. THE CTLR INFORMED ME THAT THEIR RADAR WAS NOT WORKING AND THAT THE PLT OF THE OTHER ACFT TOLD THEM HE WAS MAINTAINING 8500 FT. I TOLD THE AGENCY THE ACFT WAS NOT MAINTAINING 8500 FT BUT 8000 FT. I TOLD THEM THAT THEY NEEDED TO FILE AN NMAC RPT. ISSUES: WHY DIDN'T THE TCAS PROVIDE ANY ALERTS? WHY DID SANTO DOMINGO ISSUE A CLRNC THAT WOULD BRING 2 ACFT ON AN INTERCEPT COURSE WITHIN 500 FT OF EACH OTHER WITH OR WITHOUT RADAR? TRAINING: ARE WE SO RELIANT ON TCAS AND CTLRS NOW; THAT IF THIS HAPPENED IN IMC CONDITIONS (NO TCAS ADVISORY/ALERTS); WOULD WE HAVE HAD A MIDAIR COLLISION! SUM: IF WE HAD NOT STOPPED OUR CLB; WE WOULD HAVE HAD A MIDAIR COLLISION.