Fan blew up capacitor, replaced capacitor, now it won't turn
When fans get old, the lubrication on their bearings is usually gone. Most consumer grade fans have oilite bushings. These wick oil from a cotton or wool to the bushing; as they age, they use up the oil, pull more current, and may pop the cap. I have recovered many fans by using a light oil and saturating the media with oil. When starting the fan, if you give it a flick and it runs but then slows and stops, this may be your issue.