Try figuring out what LCD panel is in that device and if it can be obtained as spare part from Asia. As a screen-less device, options are limited to non-graphical stuff, i.e. servers. Portable game server (LAN parties!
), download server or even local mirror of your chosen distro. If you go the server route, stick to tried-and-tested: Debian, Slackware, Fedora (in that order, but that's personal
) If you want to learn more about Linux and what makes it tick and how it's done, try Linux from Scratch (LFS) or Gentoo. Expect a steep learning curve