The mechanism that moves the blend door is on the drivers side of the center airflow box. You could at least look at that to make sure it is moving when the cable is moved.
It could be that the cable is just not adjusted quite right.
If you have to actually get to the blend door, then the whole dash has to come out and the center airflow box has to be removed and taken apart. But I would doubt there is anything wrong with the blend door itself.