2001 Mitsubishi Mirage my car keeps dying

My service engine soon light came on, when I went to start my car, and the engine died. It turned on fine, but after a couple seconds, it slowly lost power and died. But if we leave it sit for a while, it starts, then runs. But we cant turn it off once its on, or it wont start again. When I was driving, the car stayed on, but the gas petal didnt work. Then it just started working again. We replaced the fuel filter, and the fuel pump, and the screen in the tank, but its still dying. What can cause a car to start, but dye after a couple seconds, but sometimes, it works fine. And what can make the car stay on while driving, but make the gas petal not give gas to the car, but then just start working again. Thank you