When a broker urged them to look at 264 Glen Avenue in Millburn in 2012, their long search ended. “It was gorgeous,” Mr. Hicks said. Bay windows let in glorious light, and French doors graced the living room. The front yard had a stream running through it with a footbridge, and the house looked out into the thick woods of the South Mountain Reservation, whose southern tip began just across the street.

They offered the seller’s asking price of $650,000, and “she just took it,” Mr. Hicks recalled. In retrospect, he said, “That should have told us something.”

Once they moved in, problems quickly mounted. New windows had been installed in some rooms, but haphazardly, without insulation. A contractor told them that the previous owner had removed a load-bearing wall without putting a hefty beam across the ceiling to make up for the missing wall. “Nothing was shoring up the second floor,” Ms. Hicks said. An electrician told them the wiring was not grounded, and that a fire could break out at any time.

The basement had a tankless water heater, a selling point for the Hickses. But shortly after they moved in, it stopped working. It was supplying water to a Rube Goldberg series of pipes that traveled all the way to the attic and then into the rooms for the radiators, looping throughout the house and covering so much distance that the water cooled by the time it got to where it was needed. During last year’s often bitter winter, the radiators couldn’t get the second floor warmer than 48 degrees. Ms. Hicks said she was working from home, “but with a hat on” and a space heater glowing.