2001 Oldsmobile Alero engine stall

My alero has not been starting. When you turn the key the engine sounds as if its not getting gas and will just crank and crank. I have a remote start in the car and when I use that it will start right up with out hesitation. I had the ignition switch replaced and that has not fixed the problem. It has now started to turn off while i'm driving. It does not sputter and stall but it just cuts off as if you turned the key off. It does not seem to be consistent with anything I do. Such as turning on a blinker or putting on the brake. Just driving straight down a road it will cut out.