Car keeps dying

My car just keeps dying while I am driving. I'll be driving and it's like the engine just shuts down. The lights and radio still come on, but it won't start. If I let it sit for a few hours it will start but it will only drive for about a minute before it dies again. When I try to start it after it dies, it starts shaking badly. The water pump was leaking and I had it changed, but the car dying started after I found out about the leaky water pump.