If your distributor is bad your engine will not start or run. If the distributor is going bad you'll have an engine misfire, the car will be hard to start or not start at all and you might notice some unusual noises coming from the engine.
Usually it's the distributor cap and rotor that fails the most often so I would check the distributor cap and distributor rotor first for any carbon buildup or places where it has shown to be misfiring.