MIT, Caltech, Harvard, Princeton; Do I stand a chance?

<p>I'm an international student applying to the schools named above. I'm vast in Math and science -up to third year university level, best graduating student, 6 A's and 2 B's in my senior leaving exams, 8 A's in my school's final exams, multiple prizes, lots of work in my school, programmer in 4 languages, very strong in English Language(best in my school), first time taking standardized tests.
The problems are: my school doesn't publicize itself much so I'm hardly able to go for any competitions, so all my accolades are limited to school stuff. I don't go out much, Also, I had only a week to prepare for Dec SAT 2s and my scores : Math2 750, Chem 750, Phy 780.
I'm taking the SAT1 in January.
Please do you think I'm wasting my time or do I still have a chance?</p>