1994 Pontiac Grand Prix starter & lights, gauges

My 94 Grand Prix will not start all the time. Starter problem I'm sure. I can start it with a hammer hit. But, about the same time my lights started dimming off and on and turn signals running slow and dim. Also, The gauges will go iratic. I've replaced the alternator with no success. If the car ignition is off the lights will stay bright. Can the problems with the lights be caused by a short in the starter since they come from the same fuse box under the hood.