Have you tried the advice: http://doc.slitaz.org/en:guides:xorg-xvesa ?
On my acer aspire laptop Slitaz stable 3.0 booted to a command prompt and to fix it I had to install the proper drivers for my video card. I used tazx and then tazhw detect-pci while logged in as root, and then I logged out of root (CTRL-D, i think or exit) and then logged in as tux and executed startx. It went thru the tazx dialog again I suppose to configure Xorg for the user tux and booted into the GUI. I had a problem with my wireless but that is another story.
Anyway it is worth a try. And for the record there are various logs created at boot up stored in /var/log you may want to look thru to see if you can spot the source of the error if tazx does not work. You can do this at the command prompt by cd /var/log to change to that directory and then ls to see what files are located there and then use nano to open the various files. Log files have an extension of .log so for example to open slim.log use nano slim.log. Good luck :)