A couple of comments. Good idea to try the new cap. To be honest I don't now what the rotation speed, if any, would occur with a shorted cap. I do know that an open in the starting circuit will yield zero rotation. Circuit breakers do sometimes weaken, that is trip at a lower current than the rating. Just an FYI though as the breaker isn't the problem. While you're in the area you may as well clean the switch contacts too. You can use a piece of 600 grit wet-or-dry paper to clean them. Hope the cap is the easy fix.
Al