A B737 CREW DID NOT ACTIVATE AN FMC RNAV RTE PRIOR TO DEP AND AFTER TKOF DEVIATED FROM THE RNAV ROUTING. THE PF HAND FLEW THE DEP UNTIL A NEW CLRNC COULD BE GAINED.

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OUR PUSHBACK FROM THE GATE IN LAS WAS NOT NORMAL. WE GOT A CALL FROM THE 'A' FLT ATTENDANT SHORTLY AFTER THE DOOR CLOSED THAT WE HAD AN UPSET PAX ANGRY ABOUT A FRIEND BEING DENIED BOARDING. THIS TRIGGERED AN ACARS EVENT WITH THE DOOR REOPENING. AFTER PUSHBACK; THE RAMP CTLR ISSUED US TAXI INSTRUCTIONS THAT SENT US TO SPOT A; NOT SPOT B. THE CAPT MADE THE COMMENT THAT WE WOULD BE DEPARTING RWY 25R. I CHANGED THE BOX TO REFLECT THE NEW RWY; RE-VERIFIED THE RNAV DEP WITH THE NEW WAYPOINTS; AND BRIEFED THE NEW T-PROC. WITH MY FAST FINGERS; I MISTAKENLY MISSED THE 'ACTIVE; EXECUTE' LIGHTS ON THE RTE PAGE. NEITHER ONE OF US CAUGHT THIS MISTAKE. THE DEP WE WERE CLRED FOR WAS THE SNEAD RNAV DEP. THE TKOF WAS UNEVENTFUL. OUT OF 400 FT I CALL FOR 'LNAV' AND THE AIRPLANE WAS TURNING TO THE L (HDG BUG SET FOR THE OLD RWY; NOT THE NEW RWY). I STOPPED THE TURN WITHIN 10 DEGS AND CALLED FOR LNAV AGAIN. WE BOTH REALIZE AT THAT TIME THAT THE FMC WAS NOT WORKING. WE CORRECTED TO THE R AND PICKED UP THE DEP AT THE FIRST WAYPOINT. ONCE OUT OF 10000 FT AND ALL CHKLISTS COMPLETED THE CAPT ASKED FOR AND WE WERE CLRED CONVENTIONAL NAV. THE CAPT AND DISPATCH VERIFIED THE ENRTE TERRAIN CLRNC. ABOUT 1 HR OUT OF LAS; THE CAPT STARTED CHKING EVERY PAGE IN THE FMC. HE CAME ACROSS THE RTE PAGE; GOT AN EXECUTE LIGHT AND THE FMC STARTED WORKING AGAIN. WE FLEW THE REST OF THE FLT IN LNAV; WITH CONVENTIONAL NAV BACKING UP THE FMS. THE REST OF THE FLT WAS UNEVENTFUL.