TCK?
> My latest idea is to study a certification. Has anybody done this before, and does it work? Will that help me start a career?
Maybe? I suspect it depends partly on where (the company) you want to work, partly why you haven't been able to find a job yet, and partly where you do (or want to) live.
1. The sort of company you want to work for
Some places want certifications, degrees, etc. so if you identify those places as somewhere you want to work, and they need certifications to apply, or to improve your chances, then you need the certifications.
The places I have worked, and know about (hosting, SAAS, all UNIX based), are mostly interested in what they can get out of you. What you can do for them. As a result even though I have no certifications, I've managed to do well. I did have to start out pretty low on the ladder, Tech Support for a couple of years, but with hard work and motivation I now work from home as a successful contractor/consultant. It should be noted that I've got the jobs I have ahead of people who have certifications or degrees, mostly because I have convinced the people I interviewed with that have something to give. Where you want to work I believe will be an important deciding factor in wether certification will be helpful.
2. Why you haven't been able to find a job yet
If you haven't been able to get a job yet but the reason is something other than certifications then it's questionable how much benefit certifications will help. Try to work out why you didn't get a job or where you failed. Ask the company why you applied to, they might ignore you, they might help.
Are you shy? Do you undersell yourself? Do you present badly in person (disheveled, or strong smell for example)? Do you come across as a mis-understood, hard done by and unfairly shunned by the world? (the answer to that last one is yes, subjectively, from my reading of your medium post[0]. People complaining about how hard done by doesn't look good.
I've seen skilled people fall at the last hurdle, job in the bag except for the final in-person meeting, only to blow it by being a miserable fucker.[1]
3. where you do (or want to) live
I know someone who has a tech job in NZ, it doesn't pay well. NZ is pretty small, are there enough jobs? Are your expectations and/or demands too high? I started out in London, but now work remotely further North. If I were starting out from scratch it would be much harder to get where I am today by being in a much more regional place. It's harder to climb the ladder if there's no ladder around.
Some closing thoughts.
You got a paid internship that seemed to get extended, can you get a job with that company? If not, why not? Can you get another job locally? At least that way any company you apply for will know that you're at least employable. Social Proof. You need to prove yourself. I've met great programmers without a degree (or an unrelated degree in photography) and some terrible programmers with relevant academic backgrounds, having a job and being good at it might actually help persuade people that you're any good.
It might also be that you just can't go to NZ. It sucks. I want to sail around on a yacht and live in the Mediteranean instead of the UK, but kids, a wife, elderly parents etc. make that dream constantly a bit too far away to grasp. You might need to scale your pland and dreams back, or at least move them around a bit.
Good luck.
[0] That piece came across as a priviledged muddled whinge to me and if it were me I'd delete it, or at least rework it into something with observations and then a constructive conclusion. I doubt that campaigning for universities to run courses will help, it doesn't matter if companies want CCNA or whatever, if students don't want to study them universities won't offer them.
[1] If you're not good in person, practice. Go out to user groups, learn to talk to people, and listen.