The child was diagnosed in 2015 and is in intensive care.
Specialists want a judge to allow them to avoid invasive treatment, saying the boy cannot recover and should be made as comfortable as possible.
A judge heard evidence in the Family Division of the High Court in London on Tuesday.
A consultant overseeing the boy's care said he had no purposeful movements, was thought to be blind, and was existing not living.
She said: "We don't wish to inflict any treatment and procedures on (him) where the risk and pain...outweighs the benefits he may receive."
The boy's parents disagree with the doctors' wishes and believe the doctors are giving up.
The court heard that they "lavish" the youngster with love and play gospel music and preach to him.
The parents claimed they thought their son laughed and appeared to be 'moving to exultations'.
Barrister Ashitey Ollennu, a lawyer representing the boy's parents, told Mr Justice Holman that sometimes people make unexpected recoveries.
The consultant said: "(His) parents don't leave him and it is admirable.
"Sadly, in spite of everything, (he) does not improve. (He) does not demonstrate that he benefits from any of that love and caring and attention his family lavish on him."
The consultant added that medics will continue to give the child fluid and nutrition.
The boy's parents, who have three other children, could give evidence today where the judge may make a decision.