The parts most likely to go bad in a convection oven include the convection heating element and the motor. If the oven won't turn on at all, the problem could be with the appliance controls or the electrical cord.
A convection oven differs from a conventional oven in that a fan circulates the internal heat, causing the food to cook evenly and quickly. Although convection ovens cook at a lower temperature than conventional ovens, the convective heat transfer makes up for temperature reduction. The convection heating element is the component warmed by electrical current that helps heat the circulating air that cooks the food, and if it burns out or becomes misshapen, it needs to be replaced. If the air inside the oven does not circulate, the fan blade does not easily turn by hand, there is a pungent odor or grinding noise, the convection motor that turns the fan may be damaged and need to be replaced.
Because a convection oven uses an abundance of electricity, it needs a dedicated electrical circuit. Otherwise, the device may have a tendency to blow a fuse or trip a circuit breaker. Electrical cords or plugs sometimes become damaged and need to be replaced. Problems with the timer, selector switch, thermostat or thermal cutoff usually involve appliance control repairs.