A B737-200 FLC HAD NMAC ON DEP FROM MLI.

Narrative

WE WERE GIVEN TAXI CLRNC FROM GATE TO 'TAXI TO RWY 27 VIA TXWY A.' JUST PRIOR TO TURNING ONTO AND XING RWY 23; GND ASKED US TO 'VERIFY' THAT WE WERE ASKED TO HOLD SHORT OF RWY 23; WE WERE NEVER TOLD THAT. I TOLD HIM THAT WE WERE NOT; BUT WE WILL HOLD SHORT OF RWY 23. TIMING WAS SO; THAT IF WE DID; HOWEVER; START TO CLB; WE WOULD HAVE HIT A PIPER CHEROKEE DEPARTING OFF RWY 3. AS WE FINALLY APCHED RWY 27; WE WERE 'CLRED FOR TKOF; RWY HDG.' 4000 FT ASSIGNED IN CLRNC. RIGHT AFTER I MADE MY 400 FT CALL; SOMETHING CAUGHT MY EYE OUT OF MY FAR R WINDOW. IT WAS A CHEROKEE (SAME ONE THAT DEPARTED RWY 5) AT MY 2:30 O'CLOCK POS AND ABOUT 500 FT ABOVE. THE TCASII SHOWED HIM ONLY 400 FT; THEN 300 FT ABOVE US. WE WERE BY SO FAST THAT I DIDN'T EVEN HAVE TIME TO REACT. NO AUDIO ALERT ON TCASII WAS GIVEN. I WAS VERY CONCERNED THAT NEITHER TWR NOR ATC HAD TOLD US ABOUT IT. WE WERE TOLD INSTANTLY TO CONTACT MOLINE DEP. WHEN WE SWITCHED; I HEARD THE TAIL END OF DEP TELLING SOME CHEROKEE; 'TFC NO FACTOR.' NOW I WAS FAIRLY IRATE WITH ATC. I ASKED THE PNF TO ASK WHY WE WERE NOT TOLD OF THE TFC; YET THE TFC WAS TOLD OF US -- SEEMS LIKE A B737 CAN EVADE CONFLICT BETTER THAN A SMALL PIPER. ATC SAYS THAT HE 'MISSED THAT ONE.' HE ALSO OFFERED A LANDLINE NUMBER FOR US TO RPT IT; IF WE WANTED TO. WE THANKED HIM FOR THAT; BUT ASKED HIM TO INSTEAD. WE SAID THAT HE SAW JUST AS GOOD AS WE DID AND WE WERE FAIRLY BUSY AT THE MOMENT. HE AGREED. NO OTHER CONFLICT FOR DURATION OF FLT. FLT WAS FROM LGA-MLI-DSM. I CAN'T BELIEVE THAT MOLINE TWR WOULD HAVE THE CHEROKEE MAKE A L-HAND DEP (DOWNWIND) FROM RWY 5 AND ALSO CLR US FOR TKOF ON RWY 27. WE NEVER HEARD GND; TWR OR ATC TALK WITH THEM WHEN WE WERE ON THE FREQ; OR WE MAY HAVE LEARNED HIS POS. IT MAY BE; IN MY OPINION; THAT THE PIPER MADE A MISTAKE AND WAS SUPPOSED TO MAKE R TFC. I DON'T MEAN TO POINT BLAME (MAYBE WE WERE ALL A LITTLE AT FAULT); BUT I FEEL THAT MOLINE TWR/GND SHOULD HAVE DONE A MUCH BETTER JOB SEPARATING TFC; OR JUST ADVISING OF TFC. WE COULD HAVE DONE JUST AS GOOD A JOB IN A NON CTLED/NON RADAR ENVIRONMENT! WE WERE THE ONLY ACFT AT MOLINE THE ENTIRE 20 MINS THAT WE WERE THERE -- WITH THE EXCEPTION OF 1 PIPER.