Was your father born in Illinois? And is he still alive?
If so, he can order a non-certified birth certificate which will have his biological parents’ names.
From the Illinois Dept. of Public Health website:
“Public Act 96-0895, which became effective May 21, 2010, makes it possible for an adult adoptee or surrendered person born in Illinois, who is 21 years or older, to request a non-certified copy of his or her original birth. This act also allows birth parents of adopted or surrendered persons born on or after January 1, 1946, to specify their wishes with regard to contact and to the release of their identifying information.
Request for a Non-Certified Copy of Original Birth Certificate – To find this document, go to FORMS in the right-hand column. This form is to be submitted along with a copy of a valid government issued photo identification (ID) and a check or money order for $15 made payable to Illinois Department of Public Health.”