For the State of Illinois if a father gives up all rights to a child and doesn't sign a birth certficate does he still pay?

This question has been asked and answered in hundreds of posts here.

Courts are very reluctant to grant a TPR and they will never do so just to allow a parent to get out of paying support;

If you didn't sign the birth certificate how and what are your legal rights that you feel you need to sign over?
If you are taken to court and proven by a paternity test that you are the father then NO you can't sign over rights.

If a father does not sign the birth certificate then the mother will have to prove he is the father though a court ordered DNA test.

He will have to pay child support, unless he signed his rights away to allow a step parent to adopt.