Issues with kitchen fan - how to salvage?
There's a chance the capacitor has simply failed and you can replace it. You'll have to cut one of the wires to measure it. If it has failed it will likely measure much lower than the 1.5uF capacitance marked on it or it may have large leakage due to internal damage. If it has caused the motor to overheat too much, the motor may have been damaged. The capacitor should not be getting hot at all.
In the case of a similar type of draft inducer fan used in our high-efficiency furnace the motor had to be replaced.