Is this notation for a single capacitor or a dual capacitor?
Your dead capacitor is from "Shiny Space Enterprise Co, LTD" you can find specifications from about page 10 their catalog or here. It is a single 8µF motor run capacitor. I suspect the dual terminals are there to make it possible to connect it without having to have two wires go into one terminal.

You say you've checked the fuses. I'd also check the relay's contacts haven't welded, then the cables to the fan for damage or shorts and finally see (with the power isolated) if I could turn the fan by hand.