 This phase I trial studies the side effects and best dose of heat shock protein-90 Hsp90 inhibitor AT13387 when given together with intensity-modulated radiation therapy IMRT and cisplatin in treating patients with squamous cell carcinoma of the head and neck that has spread from where it started to nearby tissue or lymph nodes. Hsp90 inhibitor AT13387 works by blocking a protein called HSP90. HSP90 helps protect cells from stress and supports many other proteins that cause cell growth. When HSP90 is blocked, tumor cell growth may be slowed or stopped and may die more easily when treated with chemotherapy and radiation. 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. IMRT is a specialized radiation therapy that delivers beams of radiation of different intensities aimed at the tumor from many angles and may kill more tumor cells and cause less damage to normal tissue. Giving Hsp90 inhibitor AT13387 with cisplatin and IMRT may kill more tumor cells. 