Will my starter coil prevent my air conditioner from working?

What is your question?

I have had my Edge about two years now and replaced my starter twice. The previous owner had installed a starter button. After the second starter everything was fine until one day I put gas in and started the car, it started hesitating almost like a hose was off. The air suddenly stopped cooling. After a few minutes it cools again then stops again. I took in for service and was told my starter coil is causing my AC to not work. What can I do to fix this problem. On the verge of trading it in.