How to Tell if your Orchid is Worth Saving
Often it is hard to tell if an Orchid is worth bringing back to life, and believe me, it is possible to bring an Orchid back usually if there are any roots or leaves left, and the middle of the plant is not rotten. There are quite a lot of techniques and tricks to use to bring an Orchid back to health, all of which I've used many times.
The best techniques to bring back almost dead Orchids is to repot into a tight pot that constrains the roots well, use good humidity with a humidity tray, and be patient. Don't forget to water as you would regularly for your Orchid. If your Orchid has no roots, you can get long plastic twist ties or wires, twist them around the base of the plant, and bend them (3-6 of these) as if they were roots, and anchor the plant well in the pot. These false roots have helped me stabilize many Orchids and help them slowly get back their health.
The time to give up on your Orchid is when the core, the part that connects the roots to the leaves, is soft, mushy, or dead.
If you have a big Orchid, or an Orchid worth a good amount of money, that is usually the time to spend a lot of extra care on getting the plant back to health. A big Orchid can often have a lot of energy stored up in the pseudobulbs, canes, or leaves and therefore come back to good health sooner, and an expensive Orchid... well is expensive so may be worth the effort.
The Orchids I usually don't feel are worth spending a lot of time saving are those worth $10-$50 that will take more than 3 years to nurse back to blooming health.