Does faulty cooling keep A/C from turning on?

What is your question?

My AC stopped working. The AC light on the dash is steady and green, no blinking. The cabin filter is fine. The fan relays are also fine. However, I drove the car on a hot Houston day on the highway and the cooling fan on the driver side did not go on. The one of the passenger side was on. Could this fan have failed and is that why the AC is not going on. I had a cooling fan fail on a Chevy Cavalier and to protect the engine the computer would not allow the AC to turn on.