Dr. Herbert Pardes, the hospital's president, described Moreno's condition when he arrived for treatment as "a complete disaster."
Both legs and his right arm and wrist were broken in several places. He had severe injuries to his chest, his abdomen and his spinal column. His brain was bleeding. Everything was bleeding, it seemed.
In those first critical hours, doctors pumped 24 units of donated blood into his body -- about twice his entire blood volume.
They gave him plasma and platelets and a drug to stimulate clotting and stop the hemorrhaging. They inserted a catheter into his brain to reduce swelling and cut open his abdomen to relieve pressure on his organs.
Moreno was at the edge of consciousness when he was brought in. Doctors sedated him, performed a tracheotomy and put him on a ventilator.
His condition was so unstable, doctors worried that even a mild jostle might kill him, so they performed his first surgery without moving him to an operating room.
Nine orthopedic operations followed to piece together his broken body.
Yet, even when things were at their worst, the hospital's staff marveled at his luck.
Incredibly, Moreno's head injuries were relatively minor for a fall victim. Neurosurgeon John Boockvar said the window washer also managed to avoid a paralyzing spinal cord injury, even though he suffered a shattered vertebra.
"If you are a believer in miracles, this would be one," said the hospital's chief of surgery, Dr. Philip Barie.
New York-Presbyterian has treated people who have tumbled from great heights before, including a patient who survived a 19-story fall, but most of those tales end sadly.
The death rate from even a three-story fall is about 50 percent, Barie said. People who fall more than 10 stories almost never survive.
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Alcides Moreno, whom his wife described as strong and athletic, may have clung to his scaffolding platform as it dropped. It is possible that the metal platform offered him some protection, although doctors said they were unsure how.
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The injured window washer spent about three weeks on a ventilator, unable to speak, and initially his only means of communication was by touch.
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He was scheduled to undergo another spinal surgery on Friday, and he will need another operation to reconstruct his abdominal wall. There is a chance he could develop complications, even life-threatening ones, during the months ahead.
Moreno will remain in the hospital for at least a few more weeks, doctors said. After that, he will need extensive physical rehabilitation. It may be another year before doctors know how much he will improve.
The medical staff was guarded Thursday about his prospects for returning to a normal life. Doctors said they believe he will walk, but they also suggested that some of his injuries are likely to be lifelong.