TinyCore -- "At 10 megabytes, Tiny Core is 1/400 to 1/100 the size of the most widely used operating systems in the world (even compared to most Linux distros). "
Quick googling shows that a lot of people managed to compile Linux kernels with networking and file system support to images as small as 300kb, also there's a 15mb fully functional distributive with GUI and stuff: http://distro.ibiblio.org/tinycorelinux/welcome.html
And all that was achieved pretty much just by removing unnecessary stuff from the stock Linux that was not made with much consideration for minimizing the image size, they obviously use all the same overall architecture and core structures.
I'd guess that the main benefit of using Assembly instead of C, assuming that you are determined to go for minimizing the size, is that it forces you to be honest about that. You will be forced to cut a lot of functionality just because it would take too long to implement it in Assembly, and "takes too long to implement" has a much more direct relationship to "too many bytes in the image" in Assembly than for C.
Here's the thing - you can already do all that stuff on a netbook. Heck, you can do it on a netbook you already own. Xpud has a boot time of 12-ish seconds, Tiny Core Linux about 9, and Moblin's pretty swift as well.
Don't quote me on those numbers because I have a terrible memory, but the point is, those operating systems are much cheaper and probably a lot better than Chrome. Much like the web browser, I don't think this operating system has anything going for it, aside from 'minimalism'.
You may want to look into Tiny Core Linux.. you don't get much slimmer than that. It's still being updated (latest build was 11 days ago).
http://distro.ibiblio.org/tinycorelinux/welcome.html
Minimum requirements from the FAQ:
> An absolute minimum of RAM is 46mb. TC won't boot with anything less, no matter how many terabytes of swap you have. Microcore runs with 28mb of ram. The minimum cpu is i486DX (486 with a math processor).
Your biggest issue is going to be media decoding. Those old processors are way too weak for youtube. Loading a modern website in a modern web browser would be hard enough on it.. streaming video with HTML5 is just too much. Streaming radio might work.. best bet would be to try to find a lightweight terminal-based music player
"Micro Core" -from the Core project- is a 8MB distro for x86.
I use it under colinux within my corporate XP netbook for gcc/make developments.
I've also tried to use it so to get an USB drive automatically publishing its linux files on windows via samba. However making a windows script smart enough to find the correct colinux parameters is a bit too tricky for me.
TinyCore is nice. I also like Zenix-os. It's just Debian, but it's setup to go OOTB. You didn't say how ancient the machine was. Bodhi is pretty minimal, and uses E17.
TinyCore - http://distro.ibiblio.org/tinycorelinux/welcome.html
Zenix - http://zenix-os.net/index.html
Bodhi - http://bodhilinux.com/
Worthlessly small? You can fit Tiny Core Linux in 12MB, which boots to a desktop. Great for a recovery drive in case your HDD becomes unbootable.
Hmm perhaps. Maybe Tiny Core Linux would work as well. At least that would keep things light.
Is potato architecture x86 compatible?
You want Tiny Core Linux. It's small, fast and has a pretty vast repo for having a relatively small userbase. It's made by one of the members of the team that made Damn Small Linux.