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It's been three weeks since Michigan declared a state of emergency in Flint, but not a single water pipe that contains lead has been replaced, NBC News has learned.

The city's utilities manager and a union official confirmed that none of the costly plumbing work has been started — even though experts agree it's the permanent solution to the crisis.

"We need to remove all the lead," said University of Michigan Professor Martin Kaufman, who is helping the city create a database of the 15,000 to 20,000 homes that have the dangerous pipes.

"It's got to be done now."

Yet, according to Harold Harrington, business manager of United Association Local 370, the plumbers union, none of his members have been dispatched for replacement jobs, which would cost thousands per home.

Instead, they have been going door-to-door as volunteers, installing water filters — a stopgap measure.

"If I need 200 guys next week, I can get them," Harrington said. "We can start as soon as I get a call."

It's a call that Oscar and Elizabeth Brown, like many homeowners in the impoverished city, aren't able to make.

Elizabeth and Oscar Brown and their granddaughter Denettra and great-grandson Dana live in a Flint house with a lead service line and fear the 3-year-old has been poisoned. Hannah Rappleye

The dusty service line that snakes out of their basement on Copeman Boulevard is made of lead, and they fear their 3-year-old -great-great-grandson Dana, who started having seizures last year, has been poisoned.

"There's no way we can afford to fix these pipes," Elizabeth Brown told NBC News on Tuesday after Harrington surveyed the property and told them it would cost close to $10,000 to correct the situation.

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"All my money is gone."

Read more about the Brown family and the pipes they can't afford to replace

Asked why no pipes had been replaced, a spokesman for Gov. Rick Snyder said the priority has been delivering bottled water and filters and the next budget plan "will call for identifying pipes and service lines that need replacing."

Flint's utilities manager, Mike Glasgow, said the city estimates there are 15,000 to 20,000 service lines that contain lead.

He doesn't have a firm figure because those records are mainly kept on index cards in a filing cabinet — many written in pencil decades ago, some with incomplete details. The city is in the process of digitizing the records.

The City of Flint's records of which water lines contain lead are mainly kept on these index cards, which officials have been trying to digitize. Hannah Rappleye

The problematic pipes include not just the old lead lines, but galvanized iron pipes in the home that soaked up lead in the water system over many years, and copper pipes installed in homes before 1987 that likely contain lead solder.

When Flint's water supply was switched from Detroit to the more corrosive Flint River in April 2014 to save money, the new chemistry began leaching lead from these pipes and depositing it in the drinking water.

Thousands of young children, the most vulnerable population, have been exposed to lead, which causes a range of mental and physical problems and can even be fatal.

Replacing the damaged pipes and making the drinking water safe again will be time-consuming and expensive, and cost estimates vary wildly.

Gov. Rick Snyder's former chief of staff, Dennis Muchmore, said in a Sept. 2015 briefing memo that it would take $60 million and 15 years to complete such a project, but that was before officials understood the scope of the disaster.

Snyder recently gave a much higher figure: $700 million. And Flint's new mayor, Karen Weaver, has said it could cost $1.5 billion.

Leeanne Walters, 36, of Flint shows water samples from her home from Wednesday to Flint's new emergency manager. Ryan Garza / Zuma Press

The city is responsible for the mains and the lines that run from the mains to a valve box, with homeowners responsible for the pipes that run from the valve box to the homes and inside the home.

"If you've got galvanized pipes that run your entire basement, that whole thing is coated with the lead that has leached into that and collected over the years," Harrington said.

"Most of the houses, over the years, they converted to copper but there are still a lot of houses with galvanized pipes."

Harrington estimates that replacing corroded pipes inside a home with newer, safer, cheaper plastic lines would cost an average of $4,000 and $6,000. And that's not counting water heaters that might need to be replaced.

It's a fantastical sum for many families in a city where the median value of owner-occupied homes is $41,700, half of households make under $25,000, and over 40 percent of households fall below the poverty line.

Scraping away the coating on a Flint water pipe reveals lead underneath. Hannah Rappleye

Church deacon Eric Tower lives next to the Browns. His house also has a lead service line leading to galvanized pipes that have been discharging water the color of tea during the water emergency.

He and his wife rely on bottled and filtered water — and he can't see laying out thousands of dollars to replace the corroded pipes.

"You wouldn't fix it in the house because it would exceed the value of the house," he said. "When we moved here 20 years ago it was a solid neighborhood, but the people who could afford to get out, got out," he added.

"So many of these homes now are rentals, or they're walking away from them," Tower said. "To put any money into the homes, it's just not a good business move."

Tower said that water had always been a bottom-line problem for residents of Flint, who pay among the highest rates in the state, an average of $140 a month.

"We were thinking that was the worst thing we were dealing with," he said. "We really thought, Flint is just gouging us with water. Never thought it was killing us. It was killing a generation."