There are several problems that would prevent the dryer from running. You could have a voltage problem, a blown thermal fuse, a broken drive belt or a problem with the door switch.
Open the dryer door to see if the inside light turns on. If not, I recommend checking the voltage at the outlet (the light bulb could be burned out). Use the diagram in the first image to check the outlet. NOTE: Do not check this live voltage yourself unless you are completely confident in your technical ability to safely measure it using a volt/ohm meter.
If the voltage is okay at the outlet, you could have a problem with the door switch (if the bulb is okay). This could prevent the dryer from running.
If the drum light turns on when you open the door, you could have a blown thermal fuse or a broken drive belt. Unplug the dryer and pull off the bottom front access panel as shown in the second image below. With this panel removed, you should be able to determine if the drive belt is broken. A switch on the motor will prevent it from running if the belt is broken. If the drive belt is okay, then you can check the thermal fuse (with the dryer still unplugged). The location of the thermal fuse is shown in the image below. NOTE: A gas dryer is shown below but the thermal fuse is in the same location on your electric dryer.
To check the thermal fuse, pull one wire off of the fuse and measure the resistance across the leads of the component. You should measure near zero ohms (continuity) if the fuse is okay. If you measure infinite resistance (open), then the thermal fuse is blown and will need to be replaced.
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NOTE: If the thermal fuse is blown, check for restrictions in the exhaust air flow in the dryer. Clean the lint screen before every load. If you use dryer softener sheets, periodically wash the lint screen with water and dry it thoroughly to remove softener sheet residue that can build up on the screen. Check the flexible vent behind the dryer to make sure that it is not kinked or clogged. Check the exhaust duct system to the outside of your home for restrictions.
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