Ask for help with aux installation in prius 2008

I have a toyota prius 2008 hatchback
with factory audio system; without Navigation system; with JBL audio system
I bought this item:

I try to install it to the right connection but when I connect all the cables of the car computer (the screen) to the radio, the aux connector stops to work and if I don't connect the computer cable to the audio system the conditioner and other things doesn't work at all I can't control on the vehicle systems like the conditioner the trip info and other.

(1) This is the cable that conect to the factory audio systemfrom the computer system (the screen):

(2) The cable from my aux system that I bought:

This is the connections of the cables in my audio system the cable that I mentioned below 1 connect to the left connector and the cable 2 connect to the right connector.

help me please to resolve this problem I need that the aux port will work well and the functions of the vehicle like the conditioner the trip info will work also.

THANL YOU
VERY MUCH
FOR THE HELP.