My first guess is bad wiring of some sort.
If your transmitter had programable channels, id suggest switching the 'broken' stick to a different channel (maybe channel 6 instead of 2). However, from a quick look, i dont believe your transmitter has that option.
Because of what the setup wizard does, the order that you attach the wires to channels doesnt matter. I would first try moving all the wires around to different channels on the reviever to try to find where the problem is.
For example, remove channel 1's wire and move each of the other wire up one channel, then place the removed wire in channel 5.
Now that each channel on the reciever has a 'new' wire on it, rerun the wizard. If a new stick refuses to register, there is likely a wire issue from the reciever to the flight controller. If the same stick still will not register, it points to a transmitter/reciever issue. Maybe the channel on the reciever is broken. Maybe the transmitter isnt sending the stick movement.
Or, moving the wires fixed a loose connection and all is now well