RAD001 With Weekly Cisplatin and Radiation Therapy in Patients With Locally Advanced Head and Neck Cancer

* Most patients receiving treatment for head and neck cancer will develop difficulty swallowing food and drinking liquids during the course of therapy. For this reason, it will be recommended that a PEG (percutaneous endoscopic gastrostomy) tube be placed in the participants stomach prior to undergoing the study regimen. This is to help maintain weight and nutritional health. * Since we are looking for highest dose of the study drug that can be administered safely without severe or unmanageable side effects, not everyone who participates will receive the same dose of RAD001 or cisplatin. * The study regimen will last for seven weeks. During each week of study participation the following will occur: Radiation will be administered each weekday (5 days per week). Cisplatin will be given intravenously at the start of each week. RAD001 will be given to the participant to take at home. Participants will take the study drug once a day in the morning starting on day 1. * A history and physical exam will be performed weekly while participant's are receiving radiation treatment. Blood tests for routine laboratory testing will be performed weekly. * Each month for the first two months after participants finish radiation therapy and stop taking RAD001 and cisplatin, they will have a physical ezam, a neurologic exam, and blood tests. X-rays, a CT, MRI and/or PET scans will also be performed a the two month visit. After the first two months, follow-up will continue every 1-2 months for the first year. Additionally, every 6 months for the first two years, follow-up visits will include an assessment of speech and swallowing functions along with X-rays, CT, MRI and/or PET scans.