Should a baby who was born brain-damaged be baptized? My priest said my baby did not need to be baptized. This has bothered me for 40 years.
Yes, of course, the child should have been baptized. All have original sin, and baptism both washes away original sin and is ordinarily necessary for salvation. The priest was incredibly wrong to deny your child baptism, so much so that you should have reported this to the bishop at the time. That said, you did your best to have your child baptized, and the child certainly is not at fault for not having been baptized. If the child is still alive, please have him baptized as soon as possible.
If your child has since passed away, please take comfort in the Church’s teaching regarding children who die without baptism. The Church says:
As regards children who have died without baptism, the Church can only entrust them to the mercy of God, as she does in her funeral rites for them. Indeed, the great mercy of God who desires that all men should be saved, and Jesus’ tenderness toward children which caused him to say: “Let the children come to me, do not hinder them,” allow us to hope that there is a way of salvation for children who have died without baptism. All the more urgent is the Church’s call not to prevent little children coming to Christ through the gift of holy baptism (CCC 1261).