Schools were told last week that the ministry was "cleansing the data for student locations" after "some deliveries have been affected by the addresses not matching where the student is based for home learning during level 3 and 4 alert levels".
Schools were asked to validate all the addresses again by April 24.
Aorere College Year 11 student Tiresa Tufue, 15, received a computer at home about a week ago but it was addressed to another student so the courier took it away again.
She and her Year 10 brother Sam, 14, have both been promised new computers this week but they have not turned up yet.
Aorere principal Greg Pierce said the ministry told him it "was aware of the error and how it occurred and that it would be rectified with the courier company immediately".
"At this stage I know some students have received them and some are still waiting unfortunately," he said.
"In addition we are providing an additional 40 Chromebooks to other needy senior students who were not on the final ministry list, which we only had 48 hours to confirm from limited information."
In the meantime Tiresa and Sam have to wait to use their mother's cellphone when they want to talk to a teacher or photograph their written work to send to their teachers, but their mother is working from home during the Covid-19 restrictions and often needs the phone.
"It's kind of frustrating and okay at the same time," Tiresa said.
"What's often frustrating about it is that we don't know when the teachers are available, we can't ask them for help. They give out tasks, we ask them questions that we need, then they leave us and do other school work.
"The good thing is that I don't have to ask the teachers all the time. I can just ask my family members and friends because they already know what the task is."
However the siblings' 11-year-old brother Falefa, in Year 8 at Māngere Central School, has been lent a school Chromebook, and on Friday the family received a modem from the Ministry of Education with a six-month free internet package.
Wakefield said the ministry had commissioned far more internet connections than computers so far - 17,969 connections ordered by April 23.
Priority for both computers and internet connections is being given to 20,000 homes where there are students in Years 11 to 13 with no existing internet, so the latest figure suggests most of this group now have or will soon have connections.
Wakefield said schools had also lent students 11,879 computers from their existing stocks.
Earlier this month he said there were 82,000 homes with up to 145,000 school-aged children without home internet. Most of those were also assumed to need computers, but all schools have checked on this list with their families.
Aorere College, whose parents are rated in the second-poorest 10th of the country (decile 2), requires all students to bring their own devices to school. It offers discounted Chromebooks for $379 from Harvey Norman and provides a letter for parents to take to Work and Income if they need a loan to buy them.
The Tufue siblings' mother, Laila Tufue, said she did buy them a Chromebook but it was lost when she had to put it in for repair.
"We had police reports, but we never got it back," she said.
As the family's sole breadwinner, she said, she could not afford to buy another one.
"I carry that guilt as a parent that I have not been able to provide the resources necessary for my children," she said.
"Do I make sure that they have uniforms so that they are not running around and hiding from teachers? Or do I make sure that they have food on the table and a warm house and a roof over their heads?
"It's juggling what's necessary and what isn't, and it has hugely disadvantaged them, particularly the older ones."
Before the lockdown, the family used computers and internet at the library and at Laila Tufue's sister's house, but both were out of bounds during the level-4 lockdown and the library is still closed.
Laila Tufue said she was "really grateful" for the free internet and the promised computers, but felt teachers had not previously realised the realities for families like hers.