When I turn the key the car starts and then immediately the engine stops. I have to push the accelerator as I am starting it to get it to keep running. Once started the car has no problems running. I am thinking its a bad fuel pump???
off hand it sounds like it needs a new fuel filter. possibly a failing fuel filter.
you could take it in to have the fuel pressure checked. ???
check engine light on?
Can you tell me why you would just guess at a very expensive part, rather than put a fuel pressure gauge on it and measure the fuel pressure?
Any novice mechanic can do it.