2006 Chevrolet Cobalt Multiple problems with

Seemingly all at once, the air conditioning started blowing warm air when we are in the traffic. Out on the highway, it will blow cold again, but as soon as we slow down it's back to warm. Also it began to start idling down when sitting still and acting like it might die. Now it does die and all this always happens when the air is on. The dealership told us we need a computer upgrade to the tune of $200 and that should fix the problem. However, they are also the ones that told us they had fixed the air when obviously it is not fixed because it's blowing warm air. We are reluctant to hand over $200 without checking the validity of this type of repair. We just simply can't afford to throw money at it until we hit on the right repair. Is there any type of diagnostic test that can definitively tell us if we really do need a computer upgrade? The other worrisome thing is that the key won't come out of the ignition anymore without reaching inside the steering column and tripping a little button up inside there. Then it pops right out but it's very annoying to have to do this every time, and we are also afraid that it might be dangerous if left this way. Any advice would be appreciated!