The lease itself - provided it has all elements of a legal contract - is binding. That said, in a situation like this I would speak to an attorney and provide detailed information so they may accurately advise you because there are some (very few) exceptions to the law.
I want to address another specific part of your question, even though quite some time has passed since it was posted, because the issue of deposits is one that is regulated by law in this state. In New Hampshire (and there are very few exceptions here) a landlord may charge a tenant one month's rent (first month) and a security deposit (not to exceed a month's worth of rent) when the lease agreement is initially created. Landlords may not charge additional money under the majority of circumstances. For example, in New Hampshire a landlord may not ask for the first month, last month, and security deposit up front. Additionally, a landlord may not ask for other deposits such as a pet deposit in addition to a security deposit equal to a month of rent and the first month of rent. If a landlord is asking for additional money, after a tenant already has a lease, I would advise contacting an attorney to find out if there are any exceptions to the law in New Hampshire that allow for that.
If you need any assistance or guidance concerning rentals or the rental process please feel free to contact me.