In the old days of weak, point type ignitions, when a car or truck would not start and someone went on a service call they ALWAYS took a distributor cap. The almost ALWAYS needed it when they got there.

I have never been able to find the cracks that caused these caps to give a no start condition, but they were always there if you looked hard enough. I would not replace the cap as an experiment, but I would inspect it closely, preferably with a magnifying glass.

Good luck,