If all the roots are dead on your Orchid or if the root is broke and just barely staying on the stem, can you cut all the roots off and start over?
Roots are necessary for your Orchid to survive.
Healthy roots should be green or light colored or even silvery.
Rotten roots are dark, soft and mushy. These can be trimmed away with clean sterile tools.
If no roots remain, the orchid will not likely survive.
Here are some articles with more information.