Appliance power cords take a lot of abuse. They are stepped on, pulled on, broken and cracked. When one fails, the appliance it is attached to also fails. Fortunately power cords are cheap and are easy to replace and rewire with a soldering iron and little else.
Look at the old power cord to determine what type of replacement to use. Does the plug have two or three prongs? How long is the cord? How thick is it? You will need to know all of these things before buying a new cord.
Inspect the appliance casing to determine how it is put together. It may be held together with screws or tabs. Remove the screws, put them aside so they don't get lost and carefully open the appliance.
Even if it's not plugged in, the appliance may still carry an electrical charge. Take a wire with an alligator clip on one end, and clip it to a metal part of the appliance chassis. Strip a half-inch of insulation off the other end of the wire, then partially unscrew the face plate to the nearest electrical socket. Wrap the bare end of the wire around the outlet screw, then screw it back in. This will ground the appliance.
Heat the soldering iron, then hold it to one of the power cord's contacts in the appliance. Pull that wire free when the solder melts; you may need needle-nose pliers for this. Note the colour of the wire; black or red is the "hot" wire, white represents the neutral connection and green--or bare wire--is the ground. Do the same for the other contact; there may be three in all. Again, note the wire colours. If there is a grommet around the power cord, remove that and set it aside.
Take the new power cord and hold it up against the old one. Then, If the cord has a split down the middle, separate the halves with a knife, using the old cord as a guide. If it's not a split cord, cut away the outer insulation from the free end of the new cord, again using the old one as a guide. Be careful; if you cut too deeply you may completely strip the inner wires. Then, strip three-quarters of an inch of insulation off the two or three wires inside the new cable.
Take one of the freshly-stripped inner wire and twist the strands of the wire together. Then, wrap that wire around the proper appliance contact and solder it in place. Do the same with the other wires, again noting the insulation colour. For screw-in connections, wind the stripped wires around the screw terminals and tighten them down. For screw-in connections the white insulated wire goes to the silver terminal, black or red wire to the gold screw and ground to the green screw.
Reassemble the appliance and test it.
Don't skimp when buying a replacement power cord; thicker-gauge wire can better handle higher-wattages than a thinner cable. If the cord is cracked, damaged, or gets hot while the appliance runs, replace it.
Do not work around live, plugged-in electrical equipment. Even when the appliance is not plugged in, some components may still carry enough electrical charge to shock you. The soldering iron is hot; handle it with respect.