On a small electrical appliance, the capacitor, wired across the motor, is there to prevent TV and radio interference. The machine will still work without this - although its best to remove it, naturally. If the motor windings are packing in though, often the motor speed will reduce before it stops working altogether - producing more smoke. The only way to really tell whats going on is to open the machine up and look for charred bits.
John, July 2009