Ok, I was under the impression that you were connecting Windows via ethernet - it appears that you are connecting wireless with Windows. If that is the case most likely dhcp is turned off on your router.
Before going any further, can you post the output of the command 'udhcpc' (as root)?
My suggestion is that you set up static ip address in /etc/network.conf. Set dhcp = no and set the static ip address to something like 192.168.1.2 (most likely the router is set to 192.168.1.1 - if not it is just bad luck!). Set the netmask to 255.255.255.0 and gateway address to 192.168.1.1 Save the config and restart eth0. If 192.168.1.2 does not work try setting it to 192.168.0.2 or 10.0.0.1.
If none of them work then there is no option but to reset the router to factory defaults and set up the static interface on Slitaz as per the manual and reconfigure adsl connection, turn dhcp on and set up your wireless interface with passwords etc.
Good luck!