I bought a house recently and the previous owners had many orchids in suspending pots around the property. A few were green, but most of them had dry yellow stems. I pulled away most of the yellow stems that were surrounding the green ones toward the centers of each bunch. There are still quite a few of them with both yellow and green stems, but because they are intertwined it is impossible to separate the healthier looking ones.

The question is whether I can resuscitate the yellow ones with proper watering or should I cut them at the base and leave the root structure attached to the healthy ones in place?

What is yellow can't be revived I'm afraid. However orchids are much hardier than we might think and will regrow from the base. They appreciate a daily shower (or two) and they might appreciate a mild dose of special orchid fertiliser. My wife just dumps them into coconut shells along with sawdust and coconut fibre, she even makes cuttings. Oh, and they don't like full sun generally.as they grow in trees in the rain forests in their natural habitat. Try re-potting, even dividing the plants at the same time.