The only orchids that I've seen with those stupid ice cube instructions are phalaenopsis. Maybe you can look that name up on the internet and see if that is what you have. What throws me off, is you saying that new plants are growing. Phals. grow up and not out, however, they can make basel kikies (baby plants). In any case, if the flower stem is dead, cut it off. If it is a phal. the main growth will bloom every year with the correct light and watering. You did the correct thing, by changing they way you where watering it. About a week ago, I was on vacation in S. Carolina and went to get something at the Krogers grocery store. I was shocked to see 75 to 100 phals. upon entering. The prices where crazy cheap, although they didn't have proper labels. These phals also had the stupid instructions to water once a week with orchids. They must have just arrived as they were in great shape. Truthfully, I bought a few and enjoyed them in the condo and then brought them home with me. Two days later I went back into the same store and the store was trying to care for them via the insturctions. They had ice in every pot and on many of the leaves (which will hurt and possible kill the leaves). Apparently the vendor wants you to kill those plants by giving you those ice cube instructions.