2004 Chevy Impala Trouble starting?

I know these cars have trouble with the security system but I don't think this is the problem given the nature of what I am experiencing. When attempting to start it begins like a normal start up, it seems as though the starter is turning over (not just hearing clicking sounds, but rather normal start up sounds) but it seems as though the ignition doesn't actually ignite. Finally after around 3-4 seconds of holding the key in the start position it makes the sound like it has started. Usually if I don't intervene the engine will bog down and stop running, I have to push the gas in a little bit to get the car to continue to run. The strange thing is that once it is started there are no problems at all, I figure it is something wrong with the fuel delivery system, but I would think that this would continue while the car is running not just at start up. Also if it is the starter this would be strange because usually starters don't start to go bad, typically they are done or they aren't anyone have any idea what may be causing my issue. I suspect a fuel pump or some sort of injection problem, but the car seems to be running perfectly once it has started.