Ice? Why ice?

Look like rot to me. I'd cut off all the dead parts so that there is only a healthy stem left. Let it callous over for a week or so (alternate method: or until you see roots) and then stick it back in some dirt. Hold off on watering completely or water far apart until signs of roots appear.

I would also suggest not watering with ice cubes. That leads to all the roots growing on the top layer of the soil. Water it thoroughly until water drips out of the bottom. Only water it once the soil has dried out. This could be anywhere from 1-3 weeks depending on the season and your location. I hope you're able to bring your plant back to health :)

Thanks y'all. I've always used ice cubes successfully as a way to limit overwatering.

I do wait until it's dry to water them, but will try giving it a good soaking after roots start to come back.

So many leaves falling off and stalk damaged like that - I would suspect overwatering.

There is always bigger chance of overwatering if using water retaining soil. If the plant is potted in fast draining mix and a container with drainage hole (is there one?) will diminish that chance considerably. That would be better way of not overwatering than using ice cubes :)

What is the light and temps like where the plant is kept?