Won't run

I started having problems when my fuel pump went out. I have changed my fuel pump and my fuel filter. After that, when it warmed up it would start bogging down and trying to die. I had to keep my foot on the gas at all times to keep it running. There was also times when I was driving it it would just randomly die without any bogging down or anything. Now it will start but it won't stay running. It will die right after it starts. I hear my fuel pump kicking on when I turn my key over and I hear it turn off when I turn the key off. But I'm not sure why it won't stay running. Before it started dying whenever I turned it on, when my engine was cold it would run fine until my engine would warm up.