 This phase I trial is studying the side effects and best dose of cisplatin given together with paclitaxel in treating patients with stage IIB, stage IIC, stage III, or stage IV ovarian epithelial cancer, fallopian tube cancer, or primary peritoneal cavity cancer. Drugs used in chemotherapy, such as cisplatin and paclitaxel, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving more than one drug combination chemotherapy and giving them in different ways may kill more tumor cells. 