This phase I trial studies the side effects and best dose of nelfinavir when given together with cisplatin and external beam radiation therapy in treating patients with vulvar cancer that has spread to nearby tissue or lymph nodes (locally advanced) and cannot be removed by surgery. Nelfinavir is an antiviral drug normally used to treat human immunodeficiency virus (HIV). Drugs used in chemotherapy, such as cisplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Radiation therapy uses high energy beams to kill tumor cells and shrink tumors. Giving nelfinavir, cisplatin, and external beam radiation therapy may work better than giving only cisplatin and external beam radiation therapy in treating patients with vulvar cancer.