Takes almost 2 hours to complete a wash cycle

I own a Kenmore HE3 washer (Model 110.44832200) that we purchased in 2004. Recently we've noticed that it takes almost 2 hours to finish a load of clothes. No error messages show up during the cycle. It appears that clean water continues to run into the wash machine while it's draining and spinning after the wash and rinse cycles. We've also noticed that the bleach doesn't drain and the fabric softner doesn't rinse completely out of its reservoir.