Symptoms of ignition module/stator problems are the same as if you were running out of gas. Usually after the engine cools off the engine will start again. But I agree with the above posters in that you should scan the codes and test the fuel pressure. Just beware that there are other ways to test the ignition module as the computers sometimes don't store codes for them. You use a heat gun and some other paraphernalia which I can't remember the names of. You might want to get a Haynes or Chiltons manual for the car too. They've got step by step diagnostics for stuff like this.
Karl