Now 8, Liam is not living with either of his parents, but rather at an orphanage facility run by Italian Social Services.
That's because in 2007, Manuela Antonelli, Liam's mother, ignored an American court order and illegally kidnapped her son.
Antonelli, now a fugitive wanted by the FBI, brought him to Italy where they lived together until an Italian court order deemed her mentally unfit to parent.
CBS News correspondent Michelle Miller reported Liam was placed in an orphanage where his fate rests in the hands of the Italian courts.
Ernie Allen, of the National Center for Missing and Exploited Children, said Liam's case is has become complicated - but shouldn't be.
He said, "The reality is that what these courts need to look at is where was the primary residence? Who has legal custody? And, why is this child in an orphanage in Italy instead rather than being with his father in the United States?"
Michael McCarty, Liam's father, was awarded primary custody by an American court after Antonelli fled the country.
However, Liam will remain an orphan until the Italian court rules on the case. And with the courts shut down on holiday, Miller pointed out, that won't happen before the end of August.
But according to Michael, getting custody of his son is like hitting "a brick wall at every turn."
Michael, who appeared on The Early Show Wednesday, said he's appealed to every court in Italy and the United States, as well as law enforcement agencies, but said he's not making inroads.
As for seeing his son, Michael said he's only permitted to visit him in the orphanage under surveillance and observation.
"It's very unusual and difficult circumstances," Michael said. "There are a lot of people around, we're in a room...It's terrible."
Michael added the U.S. government's hands are tied.
"They can't really interfere in the other country," he said. "But the issue really is that I have custody and they are ignoring those orders over there (in Italy). They have ignored every document from the United States."
Philip Segal, McCarty's attorney who came on The Early Show with Michael said law is "extremely clear" that what's happening in Italy is illegal.
Michael's estranged wife, Segal said, was "expressly ordered not to remove (Liam) from New York, and what's happening is entirely illegal."
The custody order under international law, he said, has to be enforced because Antonelli violated state and federal kidnapping laws.
Michael said, "I think if (his case) gets some attention, and people understand what's happening - the way the rights of this child are ignored - then maybe we can get somewhere."
Michael said he is hoping to gain access to someone in the American government who can exert some pressure on the Italian authorities.
"(My son) is in a very traumatic situation right now, and he is in desperate need of my help," he said. "And I need help in order to help him."
For more information on Liam McCarty, and Michael McCarty's fight for custody, visit SaveLiam.org.