Being a Kenmore, it's probably shot. They were never known for their great quality. The mineral in the tank has probably lost most of it's capacity and the timer motor sounds like it finally gave up. You could spend a lot of money trying to fix it (if you could find parts) or you could buy a new one that will be trouble free for several years down the road. In other words, it's not worth fixing.
You will probably find if you call around for repair, if someone actually does say they will fix it, they will end up trying to sell you a new one.