Don't know about a Chrysler 300 specifically, but on many vehicles the blend door is an electric motor while the vent selection is vac based. This means where the air comes out doesn't necessarily mean anything. Again none of my info is Chrysler 300 specific.
I'd tear the dash down to the blend door for the side that isn't working right, pull the electrical plug and confirm it's getting power when it should change state with the dash controls. Could be wiring, more likely motor, or the door shaft could have broken off. Doorman makes replacement doors for some vehicles and depending on how it needs to be pulled out, might have a repair kit that's usually just including some foil tape to hold it together if it has to be cut to pull the blend door out.