I have an older Kenmore dryer that has worked well for many years. Yesterday I tried to start it and it just keep clicking. It will not start and keeps clicking until you turn the timer to off. Model number 110.96292110. Thanks.

You have to do a little research here :

Remove the rear panel, and have a look as to what is going on.
Check the drive belt : is it frayed?
Is the drum running against something?
Does anything look lose or broken?

Please be careful : do not touch anything while the dryer is connected to the power.

If you can not find anything, remove the power - take the power cable out of the socket and put it on the ground.
Note down how the belt is connecting the drum and motor.
Remove the belt (by taking away the tension from the belt this is easy).
Spin the (empty) drum a couple of times by hand, as fast as possible. Is it running freely?
Spin the motor a couple of times by hand, as fast as possible. Is it running freely?

This procedure will allow you to research what is the problem in your machine.
If everything seems fine your problem may be related to either the start capacitor of the motor having a resistance leak, or the thermostat cutting out.

The capacitor is almost always located in a rounded-off flat metal container 1' long mounted against the dryer frame or one of the walls. The value (on the housing printed in " uF ") and the numbers of connected wires are important.
If you remove the capacitor (note down first how it is wired) you can take it with you to a service shop to have it checked and if needed replaced.
The thermostat is always mounted near or against the heating element. To check the thermostat you need a Volt or Multi meter, and the knowledge how to operate one.

Of course you can also come back to the board and discuss your findings!
If necessary contact me by private mail (click on my handle and follow instructions) to draw my attention. I will than reply here again.
If this helps solving your problem, than please rate this reply.

Success !

:)