I'm having problems with my car. What could this be?

I have 2002 Isuzu Axiom. I had no major problems with my car since I bought it over 4 yrs ago. I live in Arizona and we had a really cold winter this year and that's when it started. I would go out in the morning and it would take forever to start. But just in the mornings now it's anytime of the day. My husband got it diagnosed at Pet Boys and they said it's the Ignition going out but only the dealer can fix it. I called the dealer and they gave me a quote of about 300 hundred dollars but told me it could be more because that was just a quote. I just don't think that's the problem because if I turn the A.C on in my car and let it run for about 6 to ten minutes without trying to start it. It will start right up with no problems. And most of the times through out the day it will start right up might have to turn A.C on for a few minutes but once I do it's fine. I don't want to pay for something it isn't cause I just can't afford it. I also know most quotes are always higher. Will take all answers into consideration. Thank You