1996 Plymouth Voyager Engine cuts off while driving

I recently got a 96 Grand Voyager SE 3.3 liter from my aunt for free. The speed sensors needed to be replaced but the input sensor was so old that it broke off when I was trying to remove it. I have to drive the car about 30 miles an hour now but it was doing fine as a way to get me to work and run occasional errands. Until one rainy day the car began rumbling and jerking and the engine cut out.

I got a ride and talked to my aunt and she said that the fuel sensor would get wet when she had the car and she had the same problem. Went back to the car several hours later and it drove about 10 yards and cut out again. Came back the next day and got the car about halfway to my house (roughly a mile) and it cut out again so I parked it. Came back the next day and got it home after it cutting out when almost there and again right as I got to my driveway.

Basically the engine runs (doesn't sound great when it does though) for a short time then cuts out but will cut back on if I restart the car but for a progressively shorter time with each start until it just won't start at all. When it cuts out it rumbles and makes a sputtering sound like it's running out of gas. Occasionally emits a loud bang from the muffler. 'Check Engine' light will turn off, oil light will sometimes turn on (though there is plenty of oil and it is fairly clean still), battery light does not turn on and lights/radio, etc. Stay on.

From what I've been able to gather I believe it is the fuel pump but I was hoping for some advice on how to troubleshoot. The car is not worth bringing to a shop so I want to try to fix the problem myself and if that doesn't work I'll just sell it for parts.

(Sorry if my post is long but I wanted to be as detailed as possible)