Patients undergo pelvic external beam radiation therapy (EBRT) or intensity modulated radiation therapy (IMRT) 5 days per week for 5 weeks (25 fractions) with a 3-day boost in week 6, and 1 or 3 applications of low dose rate (LDR) brachytherapy in week 6 or 5 fractions of high dose rate (HDR) brachytherapy at week 4 or 5. Patients also receive triapine intravenously (IV) over 2 hours on days 1 and 11 and orally (PO) on days 2-5, 8-10, 12, 15-19, 22-26, and 29-33 within 90 minutes after pelvic irradiation, and cisplatin IV over 90-120 minutes once weekly for 5 weeks (days 2, 9, 16, 23, and 30). Treatment continues in the absence of disease progression or unacceptable toxicity.