I want to go to Cornell univ. upstate ny. if my parent makes less than 50,000 a year can i go to college ?

my question is if they make less than that amount i heard that i can go to college for free almost i wouldnt have to pay all of the money. btw i live in hartford ct, im trying to fulfil my goals to becoming a pediatrician.? any suggestions as to what i can do?