Well, firstly: people would still make them the way they do now. Some would organize and collect materials, and some would refine and make them into parts that eventually make it into computers. The whole chain would still exist, except now it would be done voluntarily. That’s it. Organized labour does not stop existing once you get rid of money. I’m sure you’ve heard of open source software projects.
Which leads into the second part of my comment: it seems to me that your real fear is that there wouldn’t be volunteers for one or several parts of the chain… at which point I have to ask you to take a step back and think about it is that you want, and what you are defending. If there are no volunteers to do a job in such a society, and the only way to get people to do it is threatening them with poverty and starvation, then it is not a job worth doing if you value human rights and dignity.
You probably didn’t catch because I edited late, but I gave some recommended reading at the end of my previous comment. To those, I’ll add David Graeber’s The Dawn of Everything and Bullshit Jobs.