Dryer wiring?

I had a stackable Kenmore washer/dryer. It was equpied with the 3 prong electrical cord. I was able to wire it to a double 30a circuit that was in my home that only had a white and a black wire and it worked for years. I recently bought a new dryer but it will not work when I wire it the same way. It will start for a minute then shut off. I wired it to another circuit that my stove was on and it works now but i need to wire it to a differnet circuit so they are seperate.