Check the microwave's outlet is supplying electricity by plugging in another appliance. The fuse or breaker protecting the microwave's circuit might have blown or been tripped by an electrical surge. Replace the fuse or reset the breaker, depending on your home, and try the microwave again. Call an electrician if you need help with fuses or breakers.
Disconnect the microwave from its power supply and wait 30 seconds. Reconnect the power and try entering your cooking instructions again. The internal computer may be scrambled or experiencing software problems. Disconnecting the power forces the oven to reset itself.
Open and close the door tightly. Your microwave oven won't start until the computer detects the door is completely shut, for safety reasons. Large containers inside the oven sometimes put pressure on the back of the door, causing a false reading. Make sure the container you are about to microwave fits entirely within the circumference of the cooking plate.
Make sure the microwave was programmed correctly. You might have selected "Defrost" or a low heat setting by mistake. Some ovens keep the settings of the previous program unless told differently. Be sure to select a high enough heat setting, enter a time and hit "Start" when you are ready to begin.
Turn off the child lock feature; your oven won't respond to any input while it's active. Hold down the "Lock" or padlock icon button on your microwave for a few seconds. The child lock stops kids using the microwave while unsupervised. Some microwave ovens are controlled differently and may require a different combination of buttons to disable the child lock.
Take the cooking plate and turntable out of the oven and wipe the floor, walls and ceiling of the oven with a soapy cloth, removing all traces of food. Wash the turntable and plate in a sink of soapy water and dry. Wipe the inside of the oven with a dry kitchen towel and return the turntable and plate. Dirt in the microwave restricts the turntable and sometimes causes arcing.