Any ideas on how to find someone you don't know?

it was revealed to me years ago that the man married to my grandmother was not my biological grandfather. at first, i could care less. there was an initial shock, yes, but i was too young to really understand. that isn't the case anymore. i've heard varying stories of who my grandpa could be, but it's all hearsay. my grandma is still alive but i'm absolutely sure she would be no help at all. my mother wants to know as much as i, but she has a ton of emotional baggage that prevents her from finding out. a house of cards kind of deal, you know? what also doesn't help is that my grandmas husband died last year. i have a right to know who this person. i wish i could lie and say i wanted to know just for the medical background purposes, but it's not just that... i'm not deluding myself thinking James Dean is my grandpa. this is a cloud that has been hanging over me for a while now. what can i i do? how can i find out who my biological grandpa is? on my family tree, i want something more than a question mark where a name should be. what can i do to locate this person?