Engine starter, celanoid, battery?

Hello,
My name is Theresa. I have a 2004 Hyunai Sante Fe with 31,000 miles. As I was driving on the highway, I noticed notices coming from under the hood as I turned the steering wheel, and the steering became progressively tougher. I figured that there was a problem with my power steering. I was running an errand (stopped car and went into Home Depot) and when I returned to my car and tried to start it, the engine would not turn over. Not even a click, click to start the car, nothing. The car was in park, but as a fluke, I turned the key 1/4, depressed the break and moved the transmission from Park to Drive and then, back to Park. The car turned over immediately.

I brought the car to the mechanic and he said the car needed a new power steering cooler.

Twice since the power steering cooler was replaced, the same thing repeated when I tried to start the car. That is, it won't turn over (no clicking noise either. Nothing, no lights on the dash. Nothing). But once I turned the key 1/4, depressed the break and moved the transmission from Park to Drive and then, back to Park. The car turned over immediately.

My battery is at 12.4 volts. I would consider replacing the battery. But all three times that the car won't start, it goes from absolutely nothing to starting immediately. Is this a problem with the ignition starter, celanoid, or battery? It is important to note that this problem only started on the same day that the power steering problem resulted. If it were a battery problem, my hunch is that I would have come across this issue prior.

Thank you!
tplbch@yahoo. Com