Could be a fuel pump issue...but the Mass airflow sensor does tell the computer how much air is being sucked into the engine, thus regulating how much fuel goes into the cylinder. If the fuel pump was bad i don't believe you would be receiving any fuel to the cylinder whatsoever. Have you ever replaced your timing belt? The reason i ask is because it sounds like something that regulates the Air/Fuel mixture is bad, whether it is a sensor or a timing belt.
Good luck man, I hope you figure it out