"The future of 4.5 million students hangs in the balance," Rajat Madhok, spokesman of the UN Children's Fund (UNICEF) in Yemen, told AFP.
A union strike over the suspension of teachers' salaries has ground education in areas controlled by the Iran-backed Huthi rebels to a halt, three years into a war between the Iran-backed rebel alliance and a government backed by Saudi Arabia.
UNICEF estimates 13,146 schools, or 78 percent of all of Yemen's schools, have been hit by the salary crunch, many of them unable to open for the first day of school.
Nearly 500 schools have been destroyed by the conflict, repurposed as shelters or commandeered by armed factions in a war that has killed thousands and pushed the country to the brink of famine.
Schools in the capital Sanaa and across northern Yemen were forced to delay the September 30 start of the scholastic year by two weeks after the rebels failed to pay teachers' salaries.
In government-held parts of Yemen, however, most schools this year opened as scheduled on October 1.
- 'Starving' teachers -
In Sanaa, 13-year-old Bashar al-Zaraji went to his school to register for classes on Sunday, but found himself looking straight at a locked door.
"I asked the school guard where everybody was. He told me the teachers were still on strike. They want their salaries," Zaraji told AFP.
"So we're living in a country where we can't study and nothing works," he said in exasperation. "What are we supposed to do?"
AFP reporters in Sanaa said younger pupils were in tears after waiting hours for their teachers to arrive, only to be left disappointed.
A handful of schools did open their doors to allow students to register for the year.
Others have taken to replacing teachers on strike with administrators loyal to the Huthi rebel movement, a measure education experts say is far from sufficient to meet children's right to education.
"It is not only the issue of whether the schools open, but the quality of the teachers," said UNICEF's Madhok.
Nearly three quarters of Yemen's educators have not been paid for 12 months, according to UNICEF.
Teachers who struggled through a year with little to no pay say they will hold firm to their strike in the year to come.
"We're starving to death and they want us to teach?" said Abdel Hakim, a teacher in Sanaa.
"It's better to leave teaching and go look for work to feed my kids," he told AFP.
Others have been moonlighting in other professions or looking to shift vocations altogether.
"For the past two years, I've gotten paid just half my old salary every two months," said teacher Mohammed Abdelrabb.
- Children at risk -
A bleeding education sector poses a major threat to the well-being of children, who are at increased risk of being recruited into militias, forced into labour or married off young, Madhok said.
The Huthis had promised teachers would be back in the classroom this school year.
The Iran-backed Huthis in 2014 drove the government out of Sanaa and south into Aden, hometown of beleaguered President Abedrabbo Mansour Hadi.
The Hadi government last year pulled the central bank from rebel-held Sanaa to Aden, a move the UN said deprived more than one million civil servants -- including teachers -- of their salaries and pushed families toward starvation.
One principal in Sanaa said she decided to open her doors to her students on Sunday, regardless of whether any teachers actually showed up.
"If they stay home that won't stop us from receiving students," she said.
But some longtime residents of Sanaa said they were at their wits' end with the crumbling of the country's infrastructure, culminating in the paralysis of education.
"Since the Huthis came to Sanaa our salaries have been stolen, so has our health care, electricity and water" said Fahmi al-Sharabi, a 35-year-old resident of the capital.
"And now our children are being robbed of their education."