A Dyson vacuum cleaner must plug into a wall outlet to receive electrical power, the same as any other manufacturer's vacuum. A break in the power cord is potentially dangerous and must be replaced if you are to continue using the vacuum cleaner. Since the plug on the power cord is moulded on, the entire power cord must be replaced. You can replace the power cord yourself, once you acquire a new plug from a hardware store or electronics shop. The procedure does not require any electrical skills, although you will need a few household tools.
Unplug the Dyson's power plug from the wall outlet. Press in on the tab at the top front of the Dyson to release the dust case. Pull the dust case off and place it aside.
Press in on the tab on the hose directly opposite the dust case tab. Pull the hose up and off the Dyson. Place the hose on the floor next to the Dyson.
Rotate the front of the Dyson toward you. Remove the screw at the top front end inside the compartment against which the dust case tab was pressed -- use a Torx screwdriver to do this.
Pull the two plastic clips at each side of the compartment door that the screw was in outward. Pull the compartment off the Dyson.
Loosen the two screws now revealed behind the compartment door with a Phillips jeweller's screwdriver. Unwind the two wires from around the screws.
Grip the power cord where it exits the rubber nozzle to the right of the screws. Pull the cord until the wires exit the rubber nozzle. Dispose of the power cord properly.
Slit 2 inches in on the outer insulation at the end of the replacement power cord. Pull the insulation back so that you can see the two wires inside.
Strip a 1/2 inch of insulation from the ends of both wires with a wire strippers. Push the two wires through the rubber nozzle until you can see them inside the compartment door, next to the screws. Wind the exposed end of a wire around each of the screws. Tighten the screws.
Place the compartment door back on and push in on both clips. Reattach the screw.
Return the hose to the top of the Dyson. Return the dust case to the front of the Dyson.