Allan Young, 36, of Wishaw, North Lanarkshire, shook five-week-old Michael Winn in 1998, after which he admitted causing grievous bodily harm to the child. Following the child's death in 2011, the charge was upgraded to manslaughter.
Mr Young went on trial at the Old Bailey, London, yesterday, where the jurors heard the child suffered cerebral palsy and curvature of the spine as a result of the shaking.
The court heard Michael's physical and intellectual development was impaired to such an extent he had trouble breathing, was blind, incontinent and could not speak. He had only a 65% chance of surviving to the age of 11.
Prosecutor Zoe Johnson, QC, said Mr Young did not mean to cause his son really serious harm but he was responsible for Michael's death.
The shaking incident happened when then jobless Young was living with his partner Erica Francis in London, He shook his baby early on April 16, 1998, jurors heard.
When Miss Francis, then 17, woke up later that day, she noticed Michael had become "all floppy" and had "staring eyes that did not focus", Ms Johnson said. She initially thought he had flu, but the next day he was still being sick.
The lawyer said: "Erica described seeing Michael lying in his crib awake but lifeless. When she picked him up, he just slumped in her arms."
She decided to call the health visitor, but before she could, Mr Young, who denies manslaughter, admitted he "may have hurt Michael" and shaken him because he would not stop crying and had been up all night with him, the court heard.
When the baby arrived in hospital, he was "pale and fitting". A CT scan revealed he had suffered bleeding on his brain and he was diagnosed with "shaken baby syndrome", the prosecution said.
He was eventually discharged from hospital in May 1998 into the care of social services. Michael was later adopted.
Ms Johnson said: "Michael was still very much alive although severely disabled and, following the assault by this defendant, Michael was left with severe brain damage."
In January 2011, his adoptive mother saw Michael's breathing had stopped and despite the efforts of medics, he died aged 12. The death was put down to a respiratory insufficiency caused by pneumonia and the curvature of the spin following the injuries.
The trial continues.