Once I installed a Linux OS on a old IBM thinkpad with a 486 with 4 megs of ram. It could of been a 386, I don't remember. If it was a 486 it would of had to have been a SX model because it had a optional math coprocessor upgrade.
I don't remember if it had 4 or 6 or maybe 8 megs, but I think it was 4 because some floppy based versions of linux wouldn't run on it. Once you get under 8 megs running linux becomes nearly impossible.
So I eventually had some bastardized versions of a floppy distro installed and I even installed some packages from a ancient slackware version. Anyways it realy realy sucked.
What I found out worked best for it was to install DOS on it, and then use kermit as a terminal emulator to connect to the serial port on my computer. In this form it was infinately usefull, I loved it like that. In order to use it as a serial terminal you need to have a null modem cable, also called a laplink (for connecting pre-built in ethernet laptops to win9x machines), but it's mostly used to connect external modems to your computer. Becarefull incorrect serial cables can screw up your motherboard, and there are several different types. Remember: null modem serial cable.
I could even launch X programs from it. My favorite was to start Quake3 via the serial terminal and I could read Quake3's comments (normally only viewed by hitting the ~ button).
I also have a ancient 486 DX based proliant server. It had a hotswappable SCSI bay with 4 1.13 gig scsi drives. Very fast drives, very good scsi controller. It was faster then even my more modern 8gig ATA drives. It made a great file server until I could afford a nicer computer harddrive.
It had 64 megs of RAM in it, and it was a 66mhz DX model. Top of the line 486. I found a old adapter with a pentium chip, forget the name of it, but it boosted the CPU speed from 66mhz to 86mhz (whoohoo!). Made a wonderfull file server, still could if I wanted to waste the electricity to run it.
I ran Redhat 7.0 on it. Gnome even ran on it just fine. Slow as all get out.
(Those Redhat versions from 7.0-7.3 are the worst distros ever made, btw, 7.3 was so-so. 7.3 should of been 7.0)
These things make great serial terminals for more modern systems. They work wonderfull for that. But I wouldn't expect much more then that. E-mail, text based browsing, telnet/ssh'ng to shell accounts, irc chat. That's about it.
A computer is a computer is a computer. 486 will still work fine, but it wouldn't be pleasent. Basicly you have a computer that gets spanked by a pocket-size computer (64megs, 200mhz strongarm cpu for a mid-range model) and even many graphical calculators!
You'd get better results with
FreeDOS!!!!!