Delayed starting

I have been having an issue with starting my car. It has a delayed start before it cranks, turns and start. During the delay there is nothing that shows it will start (I do have power to my car, radio, windows and everything work fine). I turn the key and it just seems like it is not going to start and then after fifteen to thirty seconds it starts up, sometimes it takes longer. I changed out the starter thinking that was going bad and the problem still persists. We also tried changing the starter relay and we checked the battery connections but did not find anything and still nothing is helping this issue yet. Any ideas?