This phase I trial is studying the side effects and best dose of gefitinib when given together with radiation therapy with or without cisplatin in treating patients with stage III or stage IV head and neck cancer. Biological therapies such as gefitinib may interfere with the growth of tumor cells and slow the growth of cancer. Radiation therapy uses high-energy x-rays to damage tumor cells. Drugs used in chemotherapy use different ways to stop tumor cells from dividing so they stop growing or die. Combining gefitinib and radiation therapy with cisplatin may kill more tumor cells