Make sure that the lid is closed. The washer won't start if the lid is open. A problem with the lid switch could prevent the washer from starting.
The control could be signaling an error code as described in the second image below depending on the light that is blinking. You indicated that the cycle button is blinking. If the water level light is flashing as shown in the second image below, then I recommend that you check the other lights on the control to determine the error code being signaled.
If the cycle signal is flashing as your details seem to indicate, then you could have a problem with the lid switch as indicated above.
I provided technical information for accessing the lid switch in the first image below. Be sure that you
unplug the washer
before accessing internal components. You can measure the continuity through the lid switch with a volt/ohm meter to determine if it is okay. With the lid closed, you should measure near zero ohms of resistance through the lid switch. If the lid switch is okay, then you could have a bad control board or a failed user interface control.
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If you need more help, reply with additional details and we will assist you further.
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