I am sorry to hear what happened. But the details mentioned are not adequate to understand what happened exactly. I will discuss the possibilities here. 36 weeks is near term for delivery although it is slightly early. You mention that the ultrasond for the baby was fine. Normally a cardiotocogram (CTG) is done to see the
heart rate of the baby, not ultrasonogram. So, there remains a query why the
ultrasound was done if it was actually not the CTG that had been done.
The next thing is that if the baby seemed alright, why did they opt for an emergency cesarean section. Normally a couple of
steroid shots to the mother 24 hours before the delivery help in bringing the final lung development of the baby which is otherwise unlikely to be present. So, due to emergency cesarean section probably there was no scope for the same.
At times, the baby does not cry at birth, in such a case, the heart rate is also not good. So, that could be a possibility but the question remains that when did the heart rate come down and whether that was the reason that the doctors decided to go for cesarean section. I would need to assume that a
pediatrician was present at birth and tried to resuscitate the baby. You need to talk to him to know his findings. It is difficult to comment without his findings in place.
The possibility is that inspite of resuscitative measures, the baby remained floppy and the heart rate did not catch up at all. It happens at times the child on being born through cesarean section does not get the trigger of the state change of being born by passing through the vaginal tract and hence remains dormant as it was inside the
uterus. If this condition continues, the baby is unable to survive in the outside world.
The pediatrician's observation is vital in this regard.