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This is most likely caused by a bad door switch. A quick check you can do is to bypass the door switch and see if the dryer operates. Here is a video that demonstrates gaining access to the door switch;
Always unplug or de-energize electrical equipment before removing covers or attempting service. Be careful and wear appropriate hand protection when working around sharp metal parts.
This video is for demonstration purposes only. The dryer in this video may not look exactly like yours, but the procedure is basically the same.
Once you have the dryer open (see video), locate the connector at the door switch. Unplug this connector and place an insulated piece of wire between the blue and white wires on the side opposite the door switch (see image below). After inserting the bypass, tape this connection with electrical tape and make sure it will not touch anything else. Plug the dryer back in and try starting a cycle. If the dryer starts, the door switch (part number 3406107) needs to be replaced.
Do not leave this bypass in place and continue using your dryer. This is for testing purposes only
If you do not feel confident repairing this problem yourself, then you can have it repaired at your home by a Sears technician. Here is a link for the website:
Sears Home Services
Here is a link that you may use to view the parts list diagram and for parts purchases;
Sears Parts Direct
I hope this is helpful. Check the things I have covered here, and if I may be of further assistance as more details become available, please reply to this post.