You should do further research; several of the Ivy schools look for folks that have a very similar situation and record as yourself. In fact, you remind of a person I meet at Yale, who went through a similar circumstance and came through the CC system in Houston, TX. He graduated last year, and was by all accounts, a very solid student.
My biggest counsel would be to do specific homework on each school you are interested and create a nexus towards your academic goals at it relates to each respective institution.