91 pathfinder starting problems

I have a 91 pathfinder SE. Around two weeks ago I was out running errands. I had turned off the car and went into the store. Upon coming back out I went to turn it on and it would not start. The power comes on for the lights, radio, etc but the engine will not turn over.I had the battery checked as it was just replaced and it was ok. I was able to get it started by push starting it. Over the next few days sometimes it would start and sometimes it would not start. Yesterday it ran just fine all day long, today when I went out to start it nothing happened. I even tried to push start it and it would not start. What could it be?