I currently "owe" child support due to a default judgement made against me in the State of California. Here is the situation:

At the time all of this went down, I was residing in New Jersey. I was made aware of these proceedings but was powerless because I could not afford the time or money to fly out and fight it. I tried to respond by mail but I did it the wrong way. At the end, default judgement was made against me. This was at least 3 years ago.
Now that I am residing once again in California, my license for this state will be suspended in June unless I start making payments.

I do not think I am the father and WANT a DNA test done to prove this.
What are the statutes of limitations for this, and how do I go about fighting this in court?