B737 FLIGHT CREW REPORTS TRACK DEVIATION AFTER RUNWAY CHANGE DURING THE SKEES2 RNAV ARRIVAL TO SLC.

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WHILE FLYING THE SKEES2 RNAV ARRIVAL TO SLC; WITH RUNWAY 34R PROGRAMMED AS OUR ARRIVAL RUNWAY DUE TO CLOSURE OF RUNWAY 34L; WE WERE CHANGED TO RUNWAY 35 FOR OUR LANDING RUNWAY. I SELECTED THE DEPARTURE/ARRIVAL PAGE TO PROGRAM RUNWAY 35. IN WHAT I BELIEVED TO BE OUR PROCEDURES; I ENTERED THE RUNWAY; RE-ENTERED THE ARRIVAL AND SELECTED THE PROPER TRANSITION FOR BOTH. (NO APPROPRIATE TRANSITION FOR RUNWAY 35.) AFTER EXECUTING; I WENT TO THE LEGS PAGE TO CLOSE UP THE DISCONTINUITY; BUT FOUND THAT WE HAD ALREADY FLOWN INTO A DISCONTINUITY. SINCE WE WERE IN THE -300 WITH NO MOVING MAP AND BOTH NAVIGATION SWITCHES IN NAV; WE HAD NO DISPLAY OF OUR POSITION ON THE ARRIVAL EVEN THOUGH WE HAD THE FIELD IN SIGHT. UNABLE AT THIS POINT TO QUICKLY DETERMINE OUR EXACT POSITION ON THE ARRIVAL; WE TURNED TO HEADING 161 DEGREES AND CONTINUED TO WORK THE CDU. WHILE MOVING POINTS UP TO FIND THE NEXT ONE TO THE SOUTH; APPROACH CONTROL CALLED TO ASK WHAT WE WERE DOING AND GAVE US A VECTOR. WE WERE THEN VECTORED TO THE VISUAL APPROACH; ULTIMATELY SWITCHING BACK TO RUNWAY 34R. I THINK IF I HAD PROGRAMMED THE ARRIVAL AND RUNWAY WITH TRANSITIONS; AND THEN SWITCHED TO THE LEGS PAGE TO CLOSE UP THE DISCONTINUITY PRIOR TO EXECUTING; ALL WOULD HAVE BEEN WELL AS WE WOULD NOT HAVE FLOWN INTO A DISCONTINUITY. THAT SAID; ONCE IN THE POSITION WE FOUND OURSELVES; I SHOULD HAVE IMMEDIATELY REQUESTED A VECTOR FROM APPROACH CONTROL AND EXPLAINED THAT WE WERE NO LONGER NAVIGATING ON THE ARRIVAL. AS IT WAS; SELECTING HEADING MODE AND THE COURSE OFF THE ARRIVAL PAGE DID NOT TAKE WIND INTO ACCOUNT AND TOOK US OFF COURSE. WHEN IN DOUBT; ASK. SUPPLEMENTAL INFORMATION FROM ACN 815231: ATC ASKED US WHAT ARRIVAL WE WERE ON AND I TOLD THEM WE WERE ON THE SKEES2 ON OUR WAY TO DYANN THEN ANNTY. HE SAID HE NOTICED WE WERE OFF COURSE AND INSTRUCTED US TO FLY AN ASSIGNED HEADING FOR VECTORS TO RUNWAY 35. I SHOULD HAVE IMMEDIATELY ASKED FOR A HEADING AS SOON AS THE FMC WAYPOINTS WERE DUMPED OUT. WHEN IN DOUBT; ASK. COMMUNICATION IS KEY. I CALLED SLC APPROACH AND TALKED TO THE SUPERVISOR ON DUTY. HE AGREED THAT IF THAT EVER HAPPENS; THE BET COURSE OF ACTION IS TO ASK ATC FOR A HEADING. I ASKED IF I SHOULD BE WORRIED ABOUT ANY FURTHER ACTION AND HE SAID NO.