Because your mother is deceased, you will need to talk to her family and her classmates from that time period if she was in school, or coworkers if she was working. Be prepared for people to stonewall you.
Understand that this search may prove fruitless. Why? Because your biological father might be dead, in jail, or married to someone else. There are other reasons that a father would not be in the picture other than (according to you) running away.
Your mother might have had more than one lover and simply didn't know who was the father. She might have been the victim of rape and/or incest. Your father could have been married (as I noted above). He could have been a one-night stand whose name she never really knew.