B757-200 FLT CREW ON DEP FROM DEN IN NO RADAR ENVIRONMENT RECEIVES AN RA FOR OPPOSITE DIRECTION TFC.

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DELAYED/STAGGERED (20 NM IN-TRAIL SEPARATION) DEPS DUE TO RADAR OUTAGE IN THE DENVER ATC SYS. CLRED FOR TKOF FROM DEN RWY 25 WITH AN ASSIGNED HDG OF 280 DEGS CAME FASTER THAN EXPECTED BASED UPON OUR TIMING OF THE PREVIOUS 3 DEPS; BUT CHKLISTS WERE COMPLETED AND WE WERE READY FOR TKOF. SHORTLY AFTER TKOF AND ESTABLISHED ON TWR ASSIGNED HDG OF 280 DEGS; PASSING 1500 FF AGL WITH GEAR RETRACTED AND FLAPS RETRACTED TO POS #1; I NOTICED A CONFLICTING TARGET ON TCAS AND RECEIVED A SUBSEQUENT TA PRIOR TO VISUALLY ACQUIRING THE ACFT PASSING 2000 FT AGL. CONFLICTING ACFT WAS A SMALL BIZJET NOW APCHING WITHIN 500 FT VERTLY AND CLOSING ON A NEARLY RECIPROCAL HDG. BASICALLY NO TIME TO QUERY THE DEP CTLR REGARDING TFC PRIOR TO EXECUTING THE SEPARATION MANEUVER. RECEIVED NEARLY SIMULTANEOUS ATC DIRECTED L TURN TO 220 DEG HDG AND RESPONDED TO A 'DSND' THEN A 'DSND; DSND NOW' RA AT THE SAME TIME. TFC SHOWED 400 FT HIGHER ON TCAS AND VISUAL DISTANCE ESTIMATED 1.0 MI AT CLOSEST POINT OF APCH. NO OVERSPDS WERE EXPERIENCED AND REMAINDER OF CLBOUT WAS UNEVENTFUL. LESSONS LEARNED: NEXT TIME I TAKE OFF; ESPECIALLY IN A RADAR OUTAGE ENVIRONMENTAL; I WILL DEFINITELY TAKE A LOT MORE TIME ON THE RWY TO DO A FULL; MULTIPLE RANGE TCAS SWEEP (AKIN TO A WX RADAR SWEEP) PRIOR TO DEPARTING ON AN ATC HDG CLRNC.