Phase I trial to study the effectiveness of combining erlotinib with radiation therapy with or without cisplatin in treating patients who have advanced mouth or throat cancer. Erlotinib may stop the growth of tumor cells by blocking the enzymes necessary for their growth. 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 erlotinib with radiation therapy with or without cisplatin may kill more tumor cells.