Wash cycle not working...

yes you need replace the timer

When the cycle doesn't advance, it's probably the timer or a cold-water supply problem:
It's the timer, if your washing machine fills with water and begins agitating, but the timer never advances--or if the washer is in a spin cycle and the timer won't advance. Then you need to replace the timer.

Rinse on most washers is cold water your wash cycles can be cold hot and even warm. Problem You may have is a bad water feed valve Or Timer and possible bad wire harness at motor to timer
check water valve Turn washer to regular wash cycle pull knob on will washer fill ?
if water starts to fill then change washer temp if washer has this.
if water comes out on all settings water valve is fine.
Check the water both hot and cold that it is turned on;at faucet.
Your Kenmore Most likely has a bad water valve check for hot water side clog or not working.

This assumes that you have a basic Kenmore / Whirlpool top load, direct drive, neutral drain (it doesn't spin until the pump removes most of the water) machine.

First, see the Sears parts site for your washer:
http://www.searspartsdirect.com/partsdirect/index.action

Enter your model number (###.#######) and you'll see a list of major sub-components with diagrams and parts.

Following is a Whirlpool / Kenmore service manual for top load, direct drive washers.

https://secured.whirlpool.com/Service/SrvTechAdm.nsf/2cd44500d572193285256a45004fd9d6/f7e2147fa98b28cf85257122007475cb/$FILE/L-55.pdf

Initial thoughts are that the Timer is worn / broken.

Here is a description of how to gain access to the console on these washers where you may be able to test the timer. (See the Whirlpool service manual for testing)

http://www.american-appliance.com/catalog/newsdesk_info.php?newsPath=16&newsdesk_id=131

This sounds like a bad timer. If the machine is several years old, the timer could be in need of replacement.

If you are handy, you can replace this device yourself and you should be able to obtain the part from any local Sears parts store or from the internet.

If you are not familiar with this kind of work, it would be best to have a technician replace the timer.

Suspect the timer/controller is in trouble

If the timer gets to the rinse cycle and stops,
Check the lid switch for continuity. If no continuity replace the lid switch.
If the timer continues through rinse and spin without doing either, replace the timer.

When the washer initially fills for the wash, is it only hot water entering the drum? Try switching the water temperature between hot and cold as it fills. If any of them show little or no water getting through, it sounds too easy but check to make sure water supply taps are on, and that the cold/hot fill hoses aren't reversed. Remove the fill hoses and check any of the screen filters for blockage (in the hoses and in the inlet water valve). When the machine stops and waits to fill but all you hear is a hum, it sounds like there is power going to the valve but water is not able to get through it.
Good luck!

Sounds like the timer has failed. It's a common problem.

Part number 8545379, $83.69 from SearsPartsDirect.com

not your timer / if anything its eather the water valve or the water slector switch