I know there are a lot of threads that are about the engine not starting but I didn't find any fixes in them.
So 2004 mini cooper s won't start. The battery is brand new and the voltage is good. I was driving my car and I turned if off for a minute and when I went to turn it on again it wouldn't start. I can hear the engine cranking and there is fuel in the tank. If I can feel/hear the engine turning does that mean that its not the starter?
I also noticed that the last time I started my car when it worked it took a little longer than normal to start and than it died right away, but when I started it again it stayed on. I can also here the fuel pump when I turn the car on if that makes a difference.
Does anyone have any ideas what it can be? How can I diagnose this?

 

I also say that on the ignition coil #3 the male connector is corroded. Can this prevent the car from starting?