C-TPF in Patients With Newly Diagnosed Locally Advanced Squamous Cell Carcinoma of the Head and Neck

* After the screening tests confirm the participants eligibility, study treatment will begin. * Prior to the start of study medication a port-a-cath will be inserted. This is done in the operating room and will require a separate consent form. During treatment a needle will be inserted into the port-a-cath through which the chemotherapy will be given. If the participant chooses not to have a port-a-cath, they will need to be hospitalized at Brigham and Women's Hospital to receive chemotherapy (approximately 5 days). * Participants will receive three cycles of chemotherapy. Each cycle of treatment will last 21 days. On day 1 of each cycle, they will receive cetuximab intravenously for 2 hours, docetaxel (Taxotere) intravenously for 1 hour, cisplatin intravenously for 1 hour, and 5-FU over a period of 96 hours through an infusion pump. On days 8 and 15 of each cycle, participants will receive another dose of cetuximab intravenously for one hour. * Not everyone who participates in this study will receive the same amount of 5-FU. A small group of participants will be given a certain dose of 5-FU through a continuous 4 day infusion. If they tolerate that well, the next group of people will receive a higher dose of 5-FU. This will continue until we can find the highest dose of the drug that can be given safely. * Participants will be seen once a week in the clinic for a physical exam. At this time vital signs will be checked and participants will be asked general questions about their health and specific questions about any problems they might be experiencing. Blood tests will also be performed at this time. * Within two weeks of completion of the third cycle of chemotherapy, participants will return to the clinic for evaluation. The following exams and procedures will be performed: Physical exam; blood tests; imaging of tumor (CT, MRI or PET); exam under anesthesia (EUA). * Once the participant has completed all treatment, we would like to follow-up with them regarding the status of their cancer. Follow-up appointments will occur every 4-6 weeks for the first year, every 8-10 weeks up to the second year, every 3 months for the third year, and then every 6 months until the fifth year.