Their affordable housing complex, Cypress Gardens, off U.S. 90, lost power during the storm.
"I feel stranded. I feel like I'm on an island by myself, you know? I feel disconnected from society. Can't talk to nobody. It's kind of like a helpless feeling. Kind of like being alone, that's what I feel and I'm hungry. I'm very hungry," Randolph Reyna Jr., who lives at the complex with his father, Randolph Sr., said.
The two were effectively trapped inside their sweltering third-floor apartment. The elevators were inoperable, and the elder Reyna had difficulty navigating the stairs.
"I'm 73, I'm disabled, I have Parkinson's, and I have neurosyphilis that must affect my balance real bad," Randolph Reyna Sr. said
Randolph Reyna Jr. told ABC13 he was grateful he could carry his father down the stairs if needed, but without a car and both phones dead, he said he didn't know what they would do next.
"There's nowhere I can think of that we could go," the younger Reyna said.
Dr. David Persse, the City of Houston's chief medical officer, told ABC13 his team was directed to the complex by the mayor's office on Monday after a city council member received a complaint from a tenant's family member.
Brittney Smith told ABC13 she contacted several public officials, beginning Saturday, regarding conditions in her mother's building.
"Nobody was receiving help," she said.
Persse said maintenance was knocking on each door Monday to inform residents of a cooling center they had just set up in the complex's main office using a generator. Residents acknowledged that anyone on an upper floor with a mobility issue would need to be transported to the center by first responders if maintenance could make contact.
Persse added several concerns, including those for residents reliant on electric oxygen concentrators.
Several residents said no one from the city or apartment attempted to make contact with them until Monday.
Houston Fire Chief Sam Peña said his department had to carry at least one man down the stairs Monday. His family was attempting to move him to safety, but he lived on the third floor and used a wheelchair.
Peña said the complex is one of at least half a dozen major senior complexes with dangerous conditions, including those without light or air conditioning, that his department has visited since the storm.
Houston Mayor John Whitmire accused Independence Hallapartment management and staff of "abandoning" residents.
ABC13 briefly spoke on-site with Cypress Gardens management, who Eyewitness News to a corporate phone number that didn't respond.
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SEE MORE: Mayor accuses management of 'abandoning' affordable housing residents without power after storm
Mayor accuses management of 'abandoning' housing complex after storm