Hard starting and cutting out while driving, especially under acceleration sounds like the fuel pump itself.
The pump is going to be located inside the gas tank so a lot of people opt not to do the repair themselves. It's not that big of a deal for the shade tree mechanic who uses common sense and has decent tools.
Try replacing your fuel pump as well. Also, have your throttle position sensor adjusted as this is an often over looked thing to do. I hope you do not need an egr valve or a coil pack. These items are not cheap. Go to any AutoZone. They can help you.
fuel pump buzzing is good news. That tells me its trying to work..There's a valve on the fuel rail for checking fuel pressure. There are 2 fuel filter in your fuel line too u know. Change the one near the tank and at the throttle body as well.
The fuel pump is about 80 bucks and u can access that from a door under the carpet in the trunk and get the pump out of the tank from there if that's what it is. Why does everyone put in new plugs and wires when ANYTHING goes wrong? Not that its a bad idea, but if you dint suspect electrical......ummm