I’m usually extremely modest, but I’ll be frank and straightforward here because I really just need some advice. I was sexually abused by my father from age 9-13, and though that had its own implications, the primary consequences resulted from its exposure. Anyhow, I am a very happy person (I always have been, in spite of all that I have experienced), but have, effectively, failed in high school. 
For whatever reason, I have had tremendous difficulty completing work, motivating myself to complete assignments, etc. I am highly intelligent (this is where I’m being less modest than usual… sorry), and without any preparation whatsoever, scored a 34 on the ACT and a 1530 on the SAT (the new one, out of 1600). My GPA is a 2.7, or thereabouts. I am a high school senior. I have, as I’m sure many on here have as well, long dreamed of attending a top-tier university (to be a bit more explicit, places like Yale (this is my top choice), Tufts, Columbia, Brown, UChicago, UPenn, etc.)… is there still any hope for me? What are my chances? Any advice?
Typically speaking from what I have personally seen, having really good standardized test scores but a rather sub-average GPA is not advantageous to an applicant. That being said, maybe there is a way you would be able to send an email to your admission officer explaining that you will try harder in high school and why you were unable to motivate yourself to complete assignments in high school. Another route would be having your guidance counselor address your rather difficult scenario within their recommendation letter. All this aside, it is difficult to know whether you have a good chance at these elite schools without any knowledge of your extracurriculars and socioeconomic background/race/gender.
I am Jewish, female, pansexual, from a lower middle class background. I am in a coding club, on the speech and debate team, on the varsity tennis team, play the viola, guitar, and harmonica (guitar and harmonica are self-taught), in MUN, on the school newspaper, and am co-president of my school’s Young Democrats club. The classes in which I am currently enrolled, and my grades in them, are: AP Lit (A), Gov/Econ (A), AP Calc BC (B+), and Hon. Physics (A).
My grade in calc can be attributed to my late entrance into the school I am now attending, if that makes any difference.
@lilycart72 While your standardized testing scores are impressive, colleges look at what a student has done over four years because it provides insight into how the student performs. The 2.7 GPA is going to hurt your chances of getting into a highly selective schools and almost impossible at schools with acceptance rates in the single digits. There are many excellent schools that you can succeed so I hope you have applied to schools that you will be happy and excited to attend.