I have a kenmore elite dryer model #11070972990. When I push the button to start the dryer it makes the noise like it wants to come on and then it stops and makes a clicking noise and nothing happens. Sometimes later I go to try itagain and it starts at 60 minutes and went gets to 40 minutes it stops, the clothes getlittle dried and then it won't start again please advise me what part I need to fix the dryer as soon as possible.

You have to do a little research here.

To check what is going on in your spin-dryer :

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 to 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.
Note : if everything seems fine your problem may be related to the start capacitor of the motor having a resistance leak.

It 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 how it is wired) you can take it with you to a service shop to have it checked and if needed replaced.

Of course you can also come back to the board and discuss your findings!

Success !

:)