(CBS) — A couple buying their first new home together relied on a private home inspector, city building inspectors and a warranty that came with their new $600,000 condo.

But as CBS 2 Investigator Pam Zekman found, none of that protected them from alleged construction defects, including  the heat in their home, the roof over their heads and even the air they breathe.

With Chicago in the midst of a residential construction boom, this is a cautionary tale for anyone in the market to buy.

“It was exactly what we were looking for, something modern and beautiful and we would just be able to move in,” condo owner Edgar Bernal says.

Bernal and Lisa Sromek say a private home inspection service — recommended by their Realtor – missed some big problems, finding only “minor” issues such a needed paint touch-ups.

Worse yet, the condo owners say city building inspectors also failed to protect them by approving the condo for occupancy, despite alleged design and construction defects they later found after moving in.

The couple is now suing the contractor and developer, Noah Properties, operated by Bart Przyjemski.

“Two weeks after moving in, we had very serious problems heating our house,” says Lisa Sromek.

And a maddening accumulation of snow and frost inside windows.

“Wouldn’t you be mad?” Edgar Bernal says. “You buy a home in Chicago, you’re supposed to be able to heat it.”

Five experts hired by the condo building association and Bernal for their lawsuit believe the furnace and ductwork that was installed was too small.

Reports also said there was  “substantially inadequate insulation,” and the fresh-air intake duct on the roof was installed just inches from exhausts. That could have allowed noxious gases like carbon monoxide to be sucked back into the condo living space.

“It’s a major safety hazard. It’s a significant code violation,” says private home inspector Tom Corbett. He was hired to do an inspection after the condo owners discovered problems. “It violated public health practices and procedures.”

After Bernal complained to the city, it filed a court case citing the builder for “dangerous and unsafe conditions,” including that fresh air duct, which has now been moved 15 feet away as required by code.

“There are still substantial defects in the building,” says attorney Kevin Sterling, who is representing the condo association

When asked if the Chicago building department did its job in protecting these condo owners, Sterling replies: “In my opinion they did not.”

“Anyone doing a reasonable inspection of the building should have caught a number of these defects,” Sterling adds.

The condo owners also allege in their lawsuit that their warranties were “breached.”

“The warranty provides that the home will be free of defective material and equipment and labor,” says attorney Louis Bernstein, who represents Bernal and Sromek. “And if there is an issue, then it has to be repaired, which has not occurred.”

Home inspector Tom Corbett estimates 50 percent of the  new construction projects he inspects have deficiencies missed by city inspectors, lapses he blames on lack of enough trained inspectors.

“It’s critical because there are life-safety issues at stake here,” Corbett says.

A spokesperson for the Chicago Building Department says the city has added a total of 22 inspectors since 2012, including 9 building construction inspectors. The agency has “a sufficient and highly trained inspection force to manage the increase in new construction,” the spokesperson says.

She says inspectors assigned to the six-unit condo building in this report did their jobs and after the city filed its court case, the code violations were all corrected.

Marty Schwartz, the attorney for Przyjemski and Noah Properties, says the company has an “outstanding reputation for quality and responsiveness,” and the building complies with city code.

The seller and general contractor have been “very responsive in regard to the alleged defects” and have “promptly corrected those items brought to their attention,” the attorney says.

He adds his clients believe there are no further defects, but if some are found by an independent expert the company will fix them.

Przyjemski declined our requests for an on-camera interview.

Experts say when buying a newly constructed  home you should never use a private inspector recommended by your Realtor because of the potential of a conflict of Interest.