Diseased potted roses? How can I save them?

I have two potted rose bushes that are nearly two years old. I brought them in for the winter when the weather turned cold and they promptly started growing again, as they did last winter. However, the foliage has now died down and the stems are turning black in a way that looks like it may be a disease. They're in an indoor room with a steady temp of about 65-70 degrees and one window giving them indirect, filtered sunlight. One appears to have some sort of bright yellow mold or algae growing on the soil near the base of the plant. What can I do to save my roses?