2012 Jeep Liberty Won't Start Immediately

The car won't start right away, it takes 3 tries for it to start and it only does it when the engine is cold, once it has warmed up it starts right away (it does not make a click sound). Although the check engine light is not on, I decided to take it to Sears and have them check it and they said the computer is not showing any codes, they checked the alternator twice and on one machine it showed it was fine and on another it shoed as if it was overchatging the battery. They told me it could be a solenoid inside the alternator but they are not 100% sure that will fix the problem. I don't want to spend $300 something dollars to change the alternator if there is a possiblity it won't solve the problem. HELP!!