It really depends on your particular circumstance, but generally speaking - if there was a court document saying that he should pay you - then he could owe you the money he didn't pay. However, it really depends on the circumstance and there is not enough information to make an accurate assessment. Please see a lawyer about this.
One of the first steps would be to make sure you are legally recognized as the father of the child. Please make sure to see an attorney as soon as possible. Time is of essence!
As previously stated by the other lawyers, generally speaking you do not get a jury trial for family law cases.
You might want to check out Illinoislegalaid.org. In their search box type "divorce". Illinois Legal Aid has a lot of information for people who cannot afford a lawyer. After reading it, you might decide to do the divorce yourself without a lawyer!