What you probably have in your pipes is the resin beads from the softener resin tank. Something must be really wrong for that to have happened.
I've gone through three Kenmore water softeners. My water isn't even that bad, but these softeners tend to work well for about 6 months and then stop working and regular trouble shooting doesn't seem to help. I've had it with Kenmore's plastic service happy softeners. I'm ready to buy a Fleck brand softener they seem to have a dependable reputation.
By the way, if your warranty is out of date forget it, Sears charges a heafty price per/hour to repair the softener.