do you present yourself well? are you a quick thinker? how do you interact with VARIOUS people in VARIOUS social settings (and trust me, the entire recruiting mechanism is designed to help them find this out) do you have insights and the ability to think independently? how eloquent and convincing are your arguments? how serious are you about doing investment banking? how far would you go to get a job at our bank? have you done your research? have you talked to our people? do you know the facts? and how do you interpret these facts? are you following the markets? can you grind out 100 hours a week? are you someone I would be happy to be working with at 3am ? would i consider going out for a beer with you? how confident are you? how do you promote yourself? do you have a compelling story? how do you answer tough questions and how do you push things back? do you crumble under enormous pressure or do you thrive in it? are you a honest person? do you have the analytical skills or the learning potential?
the list goes on and on and on.
it really isn't about what you did before business school. I have seen successful bankers who were professional football players, lawyers, marketers, priests (yes, priests), military veterans, engineers. and yes i have seen bankers who studied English as undergrad major.
so my answer is, everyone has a shot. everyone. but you need to get into a good school first so that you will be given the opportunity to prove yourself to them. once the interview starts, it's all about you as a person.