Hi and welcome!
You have your start problems even if the motor is cold or warm? When the engine starts it's running round or you feel some vibrations?
If the fuel pump wasn't changed, I would say this will cause the problem. You've got a new pump? Have you checked that there is no leak in the fuel system?
You can try following: ignition on - wait 3 seconds, then start. As far as I know the fuel pump will start when ignition is on, and if you wait the engine will get fuel and starts normally. If not, then there is an other problem.
