I have had 2 orchid plants that have done very well with new blooms. My one orchid just put out a new stem and was growing nicely but when it got to about 7" long, the end turned yellow and started putting out sap. This happened 2 months ago and now it just remains yellow & sappy and the leaves are still green but seem to be starting to wilt. I have it in a well-drained pot and only water when dry. It has grown and rebudded for years but now this. Do I cut off this stem? I do have pictures.

The clear sap may/may not be a problem as orchids and other plants often exude a sugary sap to attract pollinators. But the yellowing, mushy stem is indicative that something went wrong. From the photo, there looks to be some white spots. They look too small to be mealybug (which is a common pest) or perhaps secondary fungus, or even just a reflection. The flowering stem should be cut off just below the part that is yellow and soft as side shoots should appear since it is early in the season. The wilted leaves can be due to over- or under-watering. You indicated that you might have over-watered. I suggest you knock it out of the container and see if there are any rotten roots. That aside - you are doing correct by watering only when dry and then some.