Did you apply to other schools besides Cornell? Did you ever think about schools like University of Virginia or University of Georgia? The only reason why I mention these schools is because they are fairly reputable schools with "fair" grading systems with vast variety of opportunities. I chose similar schools like UVA and UGA in the Midwest...and boy, I have been milking the university for all it's worth. Even though my classes have been fairly demanding, I have been able to spend a great deal of time on my extracurriculars. For instance, I have four publications because I was able to devote that much time into research while maintaining a fairly decent GPA.
At the end of the day, I think adcoms would rather choose someone with a 3.75+ with 34+ MCAT with amazing extracurriculars over someone with 3.4+ and 34+ MCAT from Cornell with very little ec.
I would be extremely cautious if you were to eventually go to Cornell. For one, there is grade deflation. Performing well in pre-medical courses will be extremely difficult, which means you will be a heck of a lot of time studying in the library. This WILL cut into extracurricular time (i.e. research, leadership, non-clinic volunteering, clinical volunteering, etc.). There are a number of students out there that went to state schools that ended-up in top tier medical schools. And there are also a number of students who went to top-tier medical schools that got screwed because of grade deflation. Make sure you know what you are getting yourself into.