Suspect the neutral safety switch. Try starting it in neutral instead of park. If that doesn't work, be sure it's in park, then you can bypass the starter relay to see if it cranks. If it does, the engine should start if you do that with the ignition switch turned on.
To bypass the relay, remove it, then use a stretched out paper clip or piece of wire to jump terminals 30 and 87 or the two with arrows. We can do all the testing right at that socket. You'll need a digital voltmeter or test light.