Fuel pump sticks on and won't shut off

Hi, I recently bought a 1995 dodge neon 2.0 LT DOHC with 98,000 miles on it, and when we first got it we couldn't get it to turn over fast enough to start it, and we thought it was the battery, but then we realized that the base was full of gas. I already know how bad that is for the bearings and all the lubricational matter, but we realized that the fuel pump runs when you turn the key on, but it never shuts off, so therefore its flooding the engine, since it isn't the relay switch what do you think it would most likely be?