Look at /var/log/slim.log for errors as to what broke
Check this over: http://doc.slitaz.org/en:guides:faq-login

i cannot read (=understand) the log
there are about 100 lines between the logout from default user, the attempt to connect from root, and then the reconnection to default user (to get the log)

Should i send them to the distribution list ? might be more appropriate than pasting here. You are in the mailing list arent you ?

I tried to restore de file from /etc/skeleton but it still does not work

You're right,pasting here would be bad idea.
I'm not on the mailing list.
You can login with slim as regular user tux but not root?
Did you change /etc/slim.conf ?
I need to see the whole log, too many lines for pastebin.
Upload /var/log/slim.log to www.mediafire.com
No requirement to register.
Click the Share button to the right of the uploaded file.
URL with filename,click copy link button,paste here

here we go
http://www.mediafire.com/?hxu45f97gp3d959

It is likely that I modified slim.conf
I tried to restore a backup (a livecd iso) on top of the previous installation i had
trough tar -cvf - / | tar -xvf - /media/hdaX

It seems there is no way to really reinstall a modified livecd
I can still go back to a (not too old) dd backup.
(not too old but 2 months older than the livecd)
Really i am trying not to reinstall the whole thing from scratch. No big deal if i have too, but that would be half a day of work.

I use partimage for backup.
This error is part or all of problem: /bin/sh: can't open /root/.xinitrc
Check your /root/.xinitrc
If it's deleted:

root@slitaz: cp  /home/tux/.xinitrc  /root/.xinitrc

Check permissions:

tux@slitaz:~$ ls -la /root/.xinitrc
-rw-r--r--    1 root     root          681 Jun 23 23:21 /root/.xinitrc

If permissions wrong:

root@slitaz: chmod 644 /root/.xinitrc

If owner and/or group wrong:

root@slitaz: chown root:root /root/.xinitrc