1996 Chrysler New Yorker Starter

My car has intermittent starting problems. We are on our third starter in three months. The first starter was the original one, the second one burn the electrical connection between the starter and ignition, which was replaced and a different starter was installed. Now it's intermittent. I turn the ignition and the dash lights come on but nothing cranks. If I do this a few times, ultimately it will start.
It seems like there is a dead spot somewhere.
additionaly, the engine is running really rough but when we put it on the diagnostic machine it shows normal.
Any ideas?
Thanks