The lease agreement was signed 2/5/10 for move 3/1/10. On 2/20/10 Tenant now says they do not like the lease agreement and does not want to move in now. Do they have to give written notice since they have not moved in yet, and I lost the opportunity to rent this apartment to someone else. I did receive 1 mo rent and 1/2 security. My state is RI.

Yes, they do. And you are entitled to retain at least the 1 months rent. You can also hold them to the lease until you find a new tenant. Meaning they will be responsible for the rent until the tenancy is filled as long as you are making a good faith effort to find a replacement.

The lease is valid and they can not break it just because they have not moved in. They are liable for all rents till you find someone else to rent it.