2008 Jeep Patriot Won't Start

My jeep wouldn't start the other night. The lights come on, radio works, and remoteless key works. When I try to start it the radio turns off but the lights stay on. I had the battery checked and it was bad. Replaced the battery and the same problem exists. Also the dashboard says my gate is ajar but it is closed not sure if it is related. I have tried leaving the battery off to reset it no luck. I have tried both sets of keys no luck. I have tried to start it in neutral and same thing happes no radio but still have power. Don't really hear any noise from the engine. Hear a faint wheening noise and then nothing.