Good distro for 586 computer

Hi everyone! I might not write it at the right place, but here is my question: I bought on EBay a Compaq TC1000 convertible tablet pc at a low price. It has a Transmeta Crusoe TM5800 1ghz CPU and I installed +-360mb of ram on it. The trouble is that this CPU emulates a 586 cpu only... ...and most modern distros are 686 and up... I tried Mageia and even if it is supposed to be 586, it causes kernel panic. I also tried Debian 7.2 and it works at least partly, but as in the Debian way of doing things, it asks me to go online to fetch the driver I'd need to go online... Grrr! Does someone here know of a good distro to use (or that actually boots) on a 586 CPU? Thank you in advance! -Alexandre