See this page
for more specific information on Questbridge eligibility for undocumented aliens. Given your circumstances, it might be worth a try.
Getting that SAT score up a bit couldn't hurt . . . or perhaps try the ACT?
Also, research the schools on this list
to see which ones would provide need-based aid to someone in your situation. The Ivies aren't the only ones that give good aid.
Merit aid is worth a shot if you set your sights on schools where you are certain that you'd be a top applicant . . . in other words, those schools where the average applicant has stat's significantly lower than yours. Those are the schools that would consider paying you to attend. Again, lots of research to figure out which schools would extend offers of merit aid to an undocumented alien.
I believe you have some options. Best of luck to you!