2003 BMW 325 wont start

I drove my car and parked it for the night, it would not start the next morning. I had it towed to a repair shop and they stated that the battery did not pass the load test, although when checked at home, there was 13 volts showing on a 12 volt battery. they replaced the battery, i drove the car to a few places and it started, although it turned the starter a couple of times in order to start and has never done that before. i attempted to start the car this morning and nothing. It wont start again. I thought maybe it was a relay switch or a loose connection on the starter because there is no cranking noises, all the lights come on, radio comes on, but the car will not start. Lights do not dim when trying to start it, so i dont think it was the battery to begin with...any suggestions? i had it towed back to the repair shop, but i am a girl and think they might take advantage of that situation. I have never had any trouble with this car and do have regular maintance done.