Without a model number for your Kenmore dryer, it is difficult to predict your failure. There are many different types and models of Kenmore dryers. The failures that could cause this problem vary widely.
I recommend checking the breakers if you have an electric dryer. The motor will run on most Kenmore electric dryers if only 120 volts AC is supplied to the dryer. If the second leg of 120 volts AC is missing, then the dryer will not heat. This can also prevent the timer from advancing in some models. If the breakers are okay, then I recommend checking the outlet using a volt meter. You should only take this reading if you are completely confident that you can safely measure the live voltage at the outlet. The diagram below shows the voltage that you should measure from the outlet for an electric dryer.
If this tip does not help resolve your dryer problem, resubmit your question with additional details and the model number.