Phase I trial to study the effectiveness of paclitaxel, cisplatin, and topotecan with or without filgrastim in treating patients who have newly diagnosed stage III or stage IV epithelial ovarian cancer. Drugs used in chemotherapy use different ways to stop tumor cells from dividing so they stop growing or die. Colony-stimulating factors such as filgrastim may increase the number of immune cells found in bone marrow or peripheral blood and may help a person's immune system recover from the side effects of chemotherapy