Identify the reason that a lamp (lighting fixture) won't function. The most common are:Bulb burned out.
Bulb socket oxidized, burned, corroded, or otherwise broken so as to prevent proper electrical connection with the bulb contacts.
Transformer has overheated and a winding has "shorted" out or "opened" up.
The control (on / off or dimmer switch) if present, has failed.
The cord cap (plug), cord set (that which brings voltage from the wall receptacle to the fixture), or wiring between the control and the transformer or transformer to lamp socket has open, or shorted. Look for wire and insulation that is discolored, burned off, broken, etc.