07-20-2014, 10:31 PM
You've determined the shifter works OK without the cable, but not with it. The next step would be to see if the derailleur works when you pull on the cable by hand. If that is OK then there is only one variable left - the cable. It would be likely that the cable housing is kinked or there is too high friction between cable and housing. It's quite easy when the cable is detached to move the housing back and forth to check for catches or friction.