Car not cranking

About two months ago I went out one morning to crank my car and it would not crank, it is a push start. I would put my foot on the brake and the light on the push button would turn green and all the lights on the dash, the radio, the head and tail lights all work fine, but the car itself will not crank and it will not even turn over. Then it got to the point it would crank once a day but would shut off immediately after cranking and would not crank and would not turn over no more after that. We have tested the battery and starter both are fine. I replaced the alternator. We checked all the fuses none are blown. We replaced the starter relay and the fuel pump relay. Now we are just stuck on what it could be! Thanks in advanced!