Every once in a while it wouldn't start at all

About a year ago my car started getting harder and harder to start, it came to the point where I was the only person who could turn the key just right to start it. As time went on every once in a while it wouldn't start at all. I've gotten stranded multiple times, I just had to wait and keep trying after about 60 turns off the key it would start. When you turn the key the engine doesn't make a sound, it doesn't try turning over or make any strange noises all you can hear is the celanoid clicking quietly. So we followed some advice and cleaned the battery and the battery connections with a wire brush. That helped a small bit but it was coming to the point that it was way too unreliable to drive anywhere and it starts probably one every 50 turns off the key. Please help, I'd like to have some idea of what the problem is before I bring it in so I don't get totally screwed. Thank you!