1998 Chevy Cavalier All warning lights stay on

My mother's car was towed on a dolly from PA to SC. I went to start it and it cranked right up but there was grey smoke for about two minutes. All of the dash warning lights (low oil, check engine, abs, low water, etc) stay on for a long time and then gradually start going out. When you shift gears in place (reverse, neutral, drive) there is a buzzing sound behind the fuse box and all the lights come back on. After about 20 seconds they will start going out again until you shift again. I turned the car off to check some connections and tried to start it again after about 3-4 minutes. There is a knock coming from the passenger side of the engine when you turn the key on or off. The car will not start but just turns without cranking. Any ideas?