Linux Distributions like Slitaz or TinyCore?

I'm currently using an Asus Chromebox for the time being, and I like to use as little resources as possible while still being able to do everyday tasks on a computer. Right now I'm using BunsenLabs Linux

On my old computer I hopped around on many Linux distributions.I liked TinyCore (CorePlus) and Slitaz the best. I would use them on this computer, but since it's a Chromebox and it's only meant to run ChromeOS, it has some problems with those operating systems that I can't seem to fix. I've looked on Distrowatch, but I can't seem to find anything that I like.

So what I'm basically looking for is a micro-distribution that has wifi support and can run properly on a Chromebox.

I do know my way around Linux, I can comfortably use the command line, and Text based installs are no problem for me.

EDIT: To be honest, I would rather be using a Haiku nightly build, but sadly they don't work on my computer. The latest alpha release is 3 years old and it's using outdated software.

Have you considered something like Arch Linux? Architect Linux makes ease of the Arch installer and provides wireless driver install options. What is the wireless card you are using exactly?

The nice thing about Arch Linux is that you setup how everything is going to run so if you are wanting a minimal install running a light weight desktop then you select those options. Let me know if you have any further questions.

https://sourceforge.net/projects/architect-linux/

I'm not familiar with Linux, but have you tried Ubuntu or Mint?

I have used Arch before, but it doesn't work properly on this computer from what I can remember.
As for Ubuntu and Mint, not what I'm looking for.

What I am looking for, is an Install size of 500MBs or less.

Another one that I like is Porteus, I'm just waiting for the next version to be released. The beta ISOs don't seem to work properly for me.

The only issue with Quirky is for me, is installing Grub. I just can't warp my head around manually installing and configuring Grub. Grub4Dos on the other hand, simple. Sadly they don't have Grub4Dos in the repos. haha

Judging by what you are looking for would I be right in saying you are looking for a lite weight OS with the element of minimalist?

Not a complete minimalist (pretty damn close) project out there is the Solus Project, might be what you are looking for.
https://solus-project.com/

You could also try Manjaro Linux, Arch base with an aim to be like Ubuntu with codec and driver support. They do offer some nice minimalist desktops.
https://manjaro.github.io/

I guess here is the better test, have you tried installing Ubuntu or Linux Mint on your box? I only ask because if those don't work then you might be out of luck. It would be worth the shot of just installing those to see if your problem resolves and then finding out what packages those are using if they do work and apply those to your favorite distro.

The truth is devices made by Google is kind of weird. I know a lot of people don't realize this as they think the manufactures make the computer but Google has hardcore controls over the hardware used with there OS. They really are like the second coming of Apple, the only thing I question from time to time is are they worse then Apple in there values. Some would argue no, but the truth is they do far more corrupt crap with lock downs on there products then Apple has ever done. Just my two cents on why you are having the problems that you are.

I have used Solus on this, it used far too much memory for my liking though.

Manjaro, I have tried in the past, but to be quiet honest. I don't like it. I might just wait a couple months and see if Slitaz has fixed it's issues. They come out with a new ISO every week now.