1995 Dodge Stratus car stalls and won't start some times

My car has a hitching problem. From a stop if I step on the gas suddenly nothing happens, but if I step on it slowly it works fine. It also does it when switching from 4th to 5th gear. My car stopped starting dependabley when it got cold out. It starts at random now. Usually if I get the car to start it will stall unless I give it some gas and let off the acceleratot slowly. Before it stalls my headlights get dim. If I get the car warm it runs fine but still hitches. I have changed the spark plugs, fuel filter, air filter, oil and crank sensor. The person who owned it before me claimed to have changed the coil packs and it still hitches. My battery is by my tire but I am missing the fender guard so mud and water get on my battery.