One obvious mismatch is the network mask with your Slitaz and Windows. In Slitaz you have got 255.255.0.0 as the netmask and in Windows it is 255.255.255.255. The netmask among others is set by your dhcp server and I would have a closer look at your dhcp server settings. Did you get everything going by setting static addressing as suggested by mojo above...
You need to have a default gateway in the local network (which is normally your router) otherwise there is no way of knowing where to forward packets which do not belong to the local network which explains why it cannot find the DNS servers.
