If I gave up my parental rights, am I still obligated to pay child support?

Yes!!

You really need to clarify this because in actuality you can't just give up parental rights. If the mother of the child is remarried and the new husband wants to adopt and you agree, in that case your parental rights would be terminated and you would no longer owe new child support. In most cases you would still owe for any unpaid support.