@blu: Do the maths. The events are:
1) bootloader loads compressed kernel (bzImage) -- this needs 2 MB RAM.
2) bootloader loads compressed filesystem (tinycore.gz) -- this needs an additional 8 MB RAM.
3) kernel decompresses itself -- I have no exact number, but we can cautiously estimate that it will be 1-2 MB larger afterwards.
Up to this point, 2 + 8 + 1 MB = 11 MB (of your 486's 20 MB RAM) are already used, and only 9 MB are left. Probably less. And now comes
4) kernel tries to decompress filesystem (tinycore.gz). If I do that by hand, the decompressed filesystem (tinycore) needs 14.5 MB. With 11 (of 20) MB RAM already used, that is 5.5 MB "over the limit" of your hardware. The kernel cannot decompress the filesystem with the little available RAM, and aborts with an out-of-memory error.
I am sure that you can revive the 486, and put it to good use. But *not* with tinycore's relatively big (for this small amount of physical RAM) initram filesystem. You need something with a much much smaller initram filesystem, or with no initram filesystem at all.
@danielibarnes: Just out of curiosity. I boot tinycore in qemu. Sometimes I ask qemu to emulate a 486 CPU. As long as I allow enough emulated RAM (for me, 32 MB is the absolute minimum to avoid an out-of-memory error), the 486 CPU works. Did you by any chance also try 486 emulation (if yes: in which emulator software?), and can you confirm or disconfirm whether a 486 CPU works? Thank you.