Car will not start

My car has ran fine until a few months ago it started having troubles starting. My dad and i have replaced the battery, spark plugs, spark wires, and even had the starter rebuilt. It ran fine for about a week after every replacement but went back to not starting every time. Now we've run into a new issue where the only way the car turns on is without an air filter but it only runs when we give it gas and shuts off the second we let off the pedal. We can't seem to find anyone who knows what is wrong with it.