Parents of a child who sustained catastrophic brain injuries during birth at the University of Illinois Hospital settled their medical-malpractice suit against the attending obstetrician and nurses for $35 million.Though not directly party to the suit in Cook County Circuit Court, the settlement will be paid through University of Illinois funds and the school’s excess insurance policy.The $35 million amount ties a 2004 settlement for the highest ever reported for an Illinois birth injury, according to John L. Kirkton …