first please what do you use - lan, wifi, umts??? -

it might have to do something with ernias post: http://forum.slitaz.org/index.php/discussion/1925/cooking-pppd-scripts-umask-prevents-dns-resolution-as-unpriviliged-user-after-first-connection/#Item_2

Tank's for the answer, I use Nokia 3155 CDMA Modem (dial-up with gnome-ppp)...

its the error ernia describes, because resolve.conf is not updated

If your using gnome-ppp, you need to run it as root. The easiet way is to go to terminal (xterm) and type su, enter your root password (default is root) and then type gnome-ppp &. Now you can dial up and use the internet without having to be the root user at login.

You could also install the lxshortcut package, go to menu--->internet--->gnome-ppp in the menu, right click it's icon, click properties and change the command from gnome-ppp to gksu gnome-ppp and click OK. Now whenever you start gnome-ppp from the menu, it will ask you for your root password first. This makes gnome-ppp run as root like it did with the terminal trick.

you need to run gnome-ppp as root because pppd needs root privileges, but if you run browser as unpriviliged user it makes dns resolution accessing /etc/resolv.conf without root privileges.
i had issues running browser as unpriviliged user (which should be the desiderable behavior) because of http://forum.slitaz.org/index.php/discussion/1925/cooking-pppd-scripts-umask-prevents-dns-resolution-as-unpriviliged-user-after-first-connection/#Item_2
when /etc/resolv.conf is backed-up (is it correct english ? hope yes :-) ) from /etc/ppp/ip-up it loose 644 permissions and get 600, the same when /etc/ppp/ip-down restore /etc/resolv.conf, because of the wrong umask of the scripts.
i don't use gnome-ppp to dial up but i run wvdial in a terminal as root.
@mrblack234
may you post the output of

ls -la /etc/resolv.conf

?
did you browse succesfully as unpriviliged user on your first connection?
when you can't browse as unpriviliged user and your connection is up does running

chmod 644 /etc/ppp/resolv.conf

as root let you browse?
do this when ppp is already up