Battery problems.

I have a 2005 Aveo, after driving it some Saturday, it wouldn'the start. My nephews came and jumped it, I let it run for about 1/2 hour and it started fine. I was told that the battery was no good, it was 7 years old. Two days later I went that day to an auto store they said I had a bad battery. Two days later when I was going to get a new battery the car started fine. We took it to a different auto store and they said it was a bad battery. A new battery was put in and it turns over but won'the start. It was decided that the fuse on the battery cable was bad and that was replaced. The car turns over, but won'the start and I am getting no power to my auxillary items such as clock and radio. Does anyone have an idea what might be wrong?

Someone connecting the leads backwards would be my main suspect. Check all the fuses and relays as a first step.

Check all the fuses. the main box is just right behind the battery. Also there is a box in the drivers side door.