Using a small, sharp knife, scrape off a tiny portion of the cane stem. Look for green tissue in the plant matter; if there is none, then that portion of the cane is dead.
Using the pruning shears, carefully cut off the dead cane. Check for sections of green tissue as you're pruning and avoid cutting into or nicking these areas.
Pull gently on sections of the surrounding cane to see if they bend or break; cane that's dead or dying will be brittle and show a tendency to snap off from the trunk. Trim off these areas until you get to sections of healthy green tissue.
Check the roots to see if they're rotting; smell them and if there's a musty smell, remove the dead roots with the pruning shears and continue to snip off any other areas of dead tissue from the top to the bottom of the plant.