To my knowledge, most big companies hire grads regardless of their technical background. They assess you on your drive, how you get stuff done, your relationships/social skills and your analytical skills. Technical knowledge comes last, and only positions you for your first role usually... Internal training is pretty good in most big comps....
Get a technical degree and get in a company, worry abou what you wnat to be later (but be prepared to answer during an interview, but this can always change later of course)