Unplug the light from the dimmer and plug it straight into any standard outlet. If the light comes on, the problem is in either the dimmer or control board and will require professional service.
Replace the bulb first and plug it back in. If it comes on return it to use, otherwise proceed to the next step.
Replace the plug and test the light again. If it comes on, return it to service. If not, have it professionally repaired.
Cut the old plug off with wire cutters one to two inches above the plug. Pull the outer sheathing back to reveal the three insulated wires. Fit each wire into the jaws of your wire strippers about an inch from the wire's end and close them firmly to cut the insulation. Pull toward the end of the wire to remove the insulation.
Remove the screws in the flat face of the replacement plug between the prongs, and slide the cover off. Fit the cover onto the cord. Wrap the wires around the contact screws, white to the left prong, black to to the right prong and green to the green ground screw.
Tighten the screws with a screwdriver, turning them clockwise. Slide the cover onto the plug and install the mounting screws, using the screwdriver.
Unplug the light and allow it to cool. Put on a rubber glove to prevent skin oil from making contact with the inside of the light, which can cause bulbs to fail.
Grasp the light bulb and twist it counterclockwise to loosen it. Continue turning it until it rises out of the socket. Pull it from the light.
Insert the new bulb, socket end first, and align it with the light's socket. Twist the bulb clockwise to tighten it. Restore power to the light by plugging it in.
Put on rubber gloves to protect the bulb. Open the rear of the fixture, either by lifting up on a metal strap spring latch or removing a screw, depending on the brand and model. Swing the hinged door away or pull the round plate off to reveal the bulb and socket inside.
Press in and twist the bulb to release it if it has a round base. Pull it straight out if it has a rectangular base. Place bulbs that still function into a vellum envelope and store them for reuse in an emergency.
Insert the new bulb by reversing the instructions for removal. Plug rectangular bases straight in. Push and twist round-base bulbs in to lock them in place.