I have a Kenmore unit circa 2000. Worked flawlessly for the past 6 years, then suddenly no soft water.
I replaced the gasket and cleaned the venturi disk as instructed by the annimated trouble shooting guide on the
www.kenmorewater.com website. I too noticed no suction during the brining portion of the regeneration (in fact, water was flowing into the brine tank just like you reported!)
After disassembling and cleaning the venturi completely (even using pipe cleaners in the water ways and soaking in CLR cleaner) the only change that I found was that water was no longer flowing into the tank during brining. There was some sucking sound, but not what I would define as enough suction to lift water into the venturi.
Then I noticed a footnote on the annimation that stated that the flow plug on the venturi disk may not be necessary under certain water pressure conditions (none were offered.) I decided to remove the flow plug just to check it out. There was an incredible amount of suction! The brine level fell from the "6" to the "3" or about 10".
I put everything back together and ran it thru two regeneration cycles.
I will need to order the replacement flow plug for the one I removed, even though there was nothing visible wrong with it to just to make sure (it worked for years with it in, so a new one may be all that is needed).
You can go online to reference the owners manual on the Sears parts web site (http://www3.sears.com/) to determine what the part numbers are and place an order for them.
Hope this helps.