Be careful. The availability of RAships and opportunities to work with Professors can vary greatly by campus and department. I am in the humanities (I would imagine that the funding opportunities are somewhat similar to what you will find in the social sciences) at a large state school and I can't imagine how someone would just pick up the amount of money that you have described. At my institution, you would probably have to take out loans to cover the costs of the out of state tuition. Further, most people take classes for their first three years, which would make it extra difficult to pick up that kind of money in your third year.
This does not mean that your situation will be impossible. Every institution is different and it might be feasible to pick up $35,000 at your institution. However, I would strongly suggest that you make every effort to investigate the funding environment on your campus. Hopefully, there will be someone at your potential institution who can explain the financial implications of getting a PhD.