A $75 million animal shelter in Queens, the borough’s first and only public shelter, was supposed to boost adoption rates, making animals irresistible to prospective owners.

It had spacious kennels for dogs. A skylight in the adoption room. Dedicated rooms for cats to roam free. High ceilings and state-of-the-art veterinary facilities, including a dental clinic.

But before it even opened in late July, the shelter was already in trouble.

The 50,000 square-foot building, designed to accommodate 72 dogs, was tapped to take in 77 dogs displaced from a city-run Brooklyn shelter that closed for renovations. Councilman Robert Holden, who represents a part of Queens near the shelter, said he recently received photos that showed dogs penned in small kennels with shredded blankets and bedding, smeared in excrement, their water and food dishes empty and overturned.

Alarmed by the images, Mr. Holden went to see the facility, the Queens Animal Care Center, for himself.

He was greeted with an earsplitting cacophony of barking and the unpleasant odor of dog excrement, he said. The roof leaked, the ventilation was “horrendous” and “a lot of things don’t work in it,” he said.

The gleaming promise of the new facility had crashed into the messy reality of shelter work.

Rescue experts and animal welfare advocates say the situation in Queens is just one symptom of a bigger crisis: A steady stream of animals in need of homes coupled with stagnant adoption rates is pushing the city’s shelters toward a breaking point.