The programme found that despite millions of pounds being spent on tackling the issue, the Warners were still living in poverty and were even less optimistic for their children's futures.
Three academics were asked to calculate the opportunities for children growing up in poverty in the family's community.
David Egan, professor of education at University of Wales Institute, Cardiff (Uwic), said families like the Warners needed to believe education could be a way out of poverty for their children and grandchildren.
But he warned that nearly 70% of young people in the area would not get the qualifications normally associated with future success.
"Of these about one half - overall, a third of young people - will not have achieved a basic level of qualification. These figures are likely to include virtually all of the 30-40% of young people in the area who live in child poverty.
"The consequences for these young people will almost certainly be that the poverty that they have grown up in will be something that they cannot escape and that they will pass as an undesirable legacy to their children.
"Despite their best efforts, the schools they have attended have been unable to break the almost symbiotic link that exists in the lower Cynon Valley, between socio-economic disadvantage and low educational achievement."
Michael wants to become a policeman
The report concluded the assembly government had a number of innovative education policies to tackle child poverty.
But it said there was a "compelling case" for more integrated planning, delivery, monitoring and evaluation of policies.
Professor Siobhan McLelland, a health economist at the University of Glamorgan found large differences between life expectancy in the Warner's community and the Welsh average.
She found people's lives were affected by higher rates of cancer, heart disease and diabetes.
"In the area in which the Warner family live a woman can expect to live for 76.2 years and a man 72.4 years," she said.
"Whilst this is not the lowest life expectancy in Wales, it is nonetheless significantly lower than in other areas.
"Even within Rhondda Cynon Taf itself the life expectancy in one of the least deprived wards, Llantwit Fadre, is 83 for women and 79.2 for men.
MISSING THE GRADE
The percentage of children not meeting the expected grade in the lower Cynon Valley:
Age seven -
Age eleven -
Age fourteen -
Age sixteen -
Source: Poverty in Wales report
"In other parts of Wales this is even more striking - in Bodelwyddan (Denbighshire) a woman can expect to live to 90.7 and a man 82.4," she said.
A clear difference between neighbouring communities was also found.
Professor Dave Adamson, a sociologist at the University of Glamorgan said if the family lived just a few miles away in Mountain Ash, their chances in life would be much better.
"The health scores are much better, there's about half the number of people on incapacity benefit and twice as many people get to university and it is within a stones throw," he said.
"Public expenditure in areas like this (Perthcelyn) tend to be like sticking plasters on gaping wounds rather than really solving problems.
"I think Perthcelyn is a very good example of where services are pretty much as they were ten years ago."
The report concluded: "Families living in similar places and with similar incomes to the Warner family will experience considerably reduced life chances and will not enjoy the typical experience of being a citizen in Wales and the UK in the first quarter of this century."
On Thursday, the social justice minister Brian Gibbons launched a joint agreement to help meet the child poverty reduction targets.
Eight organisations, including the Sports Council for Wales and the Welsh Local Government Association, were the first to sign the document between the assembly government, public and voluntary organisations.
Speaking at the launch, Dr Gibbons said: "Poverty affects children's lives in a multitude of different ways and therefore the solution is also multi-faceted.
"It will require a commitment from organisations across Wales to ensure that all children and young people get a chance to fully participate in community life.
"No one organisation can achieve this alone."
A spokesman for the assembly government said 100,000 children in Wales had been taken out of poverty since 1997 - a greater proportion than that in England.
"However, we recognise that 29% of children remain in poverty and this remains a major challenge for the assembly government," he said.
"It is for this reason that we have introduced a measure to bring in a new Welsh law which makes tackling child poverty a top priority.
"The assembly government has a wide range of policies and programmes and new initiatives operating across Wales aimed at tackling child poverty.
"These include employment support programmes, childcare initiatives, education and health programmes and Communities First interventions.
"We know that education is absolutely key if children and young people are to have the chance to be lifted out of poverty.
"Our multi-million pound RAISE programme is tackling the link between socio-economic disadvantage and educational under-achievement to improve the life chances of the most disadvantaged learners in Wales."
Week In Week Out: One Family in Wales is on BBC ONE Wales at 2100 on Thursday.
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