Chances?

Would my 34 act score expiate the fact that I will only have 2 AP scores by the time I apply to Cornell? At my school you start sophomore year with AP classes. I took at least three honours classes each year, but I am a year behind in history so that has really messed up my schedule. I plan to take four more APs my senior year. Also, my gpa unweighted is 3.9. I know extracurriculars play a role, but based just on what I have written here, would my application get tossed? Should I bother? Thanks for your input.