Is there an easy to find linux that i could put on a machine previously running ms dos (it's 15-16 years old i think)?

you can try Vipsosys or Damn small linux. beside... linux doesnt support DOS/Fat/Fat32 partition.

What are the system specs? What model processor? How much RAM, How much hard drive space? Do you have a CD-ROM drive or a network card?

Of modern (usable) Linux distributions, Slackware and Debian require the least amount of resources to install. Since Ubuntu is Debian for Dummies, it should work too..

You might look into qnx too.

QNX is not Linux. And it is not free. And it has very limited hardware support.

Some specs would be helpful. You should get damn small linux working on it. 15 - 16 years ago would be 1990 - 1991. So it could be a 486SX (a 486DX bastard without the floating point unit. The predecessor to the modern Celeron) with 2 - 4 MB of no parity 36 or 72 pin simms or something of that sort, though someone could have upgraded it. Damn small Linux DSL is probably the only, easy to install, Linux you'll get working on such a system.

linux doesnt support DOS/Fat/Fat32 partition.

Linux does support mounting FAT32, FAT partitions. Some distros even support installing the / partition to them, but its not recommended.

The installation process would repartition and format the / partition as ext3 anyway, so its not an issue if you are reinstalling this machine.

Probably any Linux will work, it will just run slowly. DSL will probably run well, though, and will fit nicely into available HDD space as its likely this machine has a small HDD and the minimum install for Fedora Core or SUSE is at least 700MB - 1GB I think.

Okay let me make this clear this thing has NO mouse, it is 15-16 years old, i'm lucky it has a modem, it is a zenith datasystems machine and it has a 21.6 MB harddrive, oh yes the screen only has two colors blue and white.

Well, you can't fit much anything else than DSL on that drive..

Again, what processor and how much RAM does it have? You need at least 8MB of RAM to run Linux and many kernels require you to have at least a 486 CPU. Looking at the hard drive size, you may not have these.

If you have a 386 CPU and 4 megs of RAM, you may be able to run MINIX 3.

If you have a 286 or less than 4MB of RAM (at least 2), then your only unix-like option is MINIX 2

If there's less then 2MB of RAM, then your only (usable) option is some flavour of DOS.