This study is being done to test whether panitumumab, in combination with chemotherapy and radiation is safe in people with head and neck cancer. Another goal of this study is to find the highest dose of the study drugs that can be given safely without causing serious sife effects. Panitumumab is a type of drug called a monoclonal antibody that has been studied in other types of cancers, such as kidney and colon. This monoclonal antibody is directed against the epidermal growth factor receptor (EGFR). EGFR has been found on the majority of head and neck cancer cells. By blocking EGFR, this monoclonal antibody may inhibit the growth of head and neck cancer cells.