This is a grafted rose, and as such, if the top portion grafted onto the rootstock dies, only the rootstock sends out new growth. Generally these canes are spindly, grow excessively long, and may or may not flower. If they do flower, the flowers look more like a wild type - only 1 to 2 inches across. Cutting them back will not induce them to produce the Dick Clark roses. Sometimes there is a mix of canes - some from the rootstock and some from the scion, but that doesn't sound like it from your description. If so, cutting out the reverted canes is the answer. But if you don't have any of the scion wood, the only solution is to remove the plant. Grafted roses need protection in the winter to keep the graft union from being winterkilled.