It sounds as though your blackberries have become infected with orange rust, a serious fungal disease that attacks blackberries and some black raspberries (but not red or purple raspberries). The orange powder you see is spores of the fungus. These spores spread from plant to plant on the wind. Quickly remove and destroy infected plants. Once infected, plants remain infected for their entire life, and produce no blossoms or fruit. No fungicide sprays are effective in controlling the disease. Failure to remove the infected plants risks spreading the disease to other blackberries nearby. If wild blackberries are growing nearby, remove them too. They may have been the source of the disease on your cultivated plantings. Establish new plantings from a disease-free source or from tissue-cultured plants.