08 Jeep Grand Cherokee key fob issue?

I recently damaged my key fob and purchased a new one through the dealer. I truly can’t remember if the issue I am experiencing happened before this, I don’t think it did. First issue When I turn the key, the engine starts then shuts off. Second issue I turn the key and no displays light up and I have no power door locks or windows. Third issue I turn the car on and can’t get it out of park.
It does not happen all the time and I don’t believe it happens simultaneously. Brakes Plus found no error messages on the computer. Thoughts? Similar experience?