Thanks everybody for your help and suggestions, here's the follow up:

I know that distro and it is too limited... Thanks though.

That's the first distro I tried. I followed your suggestion and tried almost all versions, down to 0.6 and all have the a 2.4 kernel.
Thanks for your suggestion, though.

This one actually worked, thank you! It's a bit too much for this limited computer (maxed out at 80MB of ram).
Excellent, that worked and looks and feels almost perfectly.

Now the problem is: find the right module to bring up the 8-bit ISA NIC. On Windows the generic "NE2000 Compatible" works, but I can't load it on Slackware, even specifying irq=3 io=0x300 (correct configuration). Maybe I need a different module? It's a generic NIC with a UMC chip.

Do you know what is the minimum RAM required to boot the live cd?

On a system with 64 MB I couldn't boot it properly. On a System with 80 MB I could.

All 16-bit ISA network cards that I tried were not compatible with 8-bit ISA, sadly.

Can you recommend any that might work?

I believe the default for the ISA NE2000 was:

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The thing is, this particular dinosaur only has an 8-bit ISA slot.

I tried a lot of cards configured with different IO addresses and IRQs, i.e.:

But none of them are cooperating on Linux, the module doesn't load.

An original Novell 2000 card didn't work, and lots of generic cards didn't work either.

Some worked on Windows 98 though, but they don't work on Linux for some reason.

I will get a 3COM card and see if it works.

Maybe it's that the NE module is not compatible with 8-bit operation mode?

Didn't you have to configure some things in bios for nic cards???

I guess I don't remember that far back.

The last Slackware version to boot in 64MB of RAM was 13.0.
I do not miss the days of setting jumpers and fiddling with ISA slot positions and BIOS settings to get cards to work.
I seem to remember using a lot of 3Com 3c509 NICs back then.