Car wont start

It turns over and cranks every time. I bought a new battery put almost half tank of gas in it, listened for the fuel pump it works. I have checked the relays, they all work, I took the cover off the fuel pump relay so that I can see it click on when I try to start it. But it wont. It wants to start. After I let it sit for a day and then go to try and start it, it starts for a few seconds, and then dies, and continues to just turn over and crank. Another question I have is, when I have the key in the on position, and press on the brake, it will not shift out of park. Is this vehicle suppose to only be able to shift out of park when the engine is running or is something wrong?