Like other microwaves, Kenmore microwaves are controlled by a number of internal components, but two major components power the device. If you have a Kenmore microwave that won't turn on, the first thing you should do is check the plug and make sure that the device is plugged in and that the outlet is properly working. If the cord is plugged into a working outlet, the reason that the microwave won't turn on is likely due to a burnt fuse.
Make sure that the Kenmore microwave is unplugged from the electrical outlet before doing any work on the microwave. Remove any loose parts of the microwave, such as the rotating plate inside the unit and place the microwave so that the door side is down on a soft surface.
Take out the 10 to 12 screws that hold the metal plate on the back of the Kenmore microwave in place with a standard Phillips screwdriver. Remove the metal plate from the back of the Kenmore microwave by sliding it toward the bottom side of the microwave. Be careful not to touch the inner components and knock anything loose.
Follow the electrical cord to the interior of the microwave to find the fuse box. A microwave fuse has a similar shape to a bulb on a strand of Christmas lights and, if the fuse is burned out, it appears brown or black inside.
Clasp the fuse gently, but firmly, and pull it up from the socket. The fuse comes free of the housing and can be removed from the microwave.
Place the replacement fuse into the microwave. Line the fuse up with the socket and press it into the space until it clicks into place.
Slide the metal plate onto the back of the microwave so that it lines up with the screw holes in the microwave's housing. Return all the screws to the metal plate to hold it into place.
Set the Kenmore microwave upright and plug the unit back in. The digital display should light up on the microwave, indicating that the unit is once again working.