ARM I: Patients receive cisplatin intravenously (IV) on days 1 and 29. Patients also undergo radiation therapy once daily (QD), 5 days a week, for 5-6 weeks. Some patients may then undergo brachytherapy over 2-3 weeks. Beginning within 8 weeks after completion of chemoradiotherapy, patients receive paclitaxel IV over 3 hours and carboplatin IV on day 1. Treatment repeats every 21 days for 4 courses in the absence of disease progression or unacceptable toxicity.