Yup change /etc/resolv.conf to a known working dns or to the routers + isp dns's.
nameserver isp dns1
nameserver isp dns2
If the cable is securely inserted into both slots and the spring clip is erect / locked then it should work. Been there done this error before
See dhcp below as some of the dhcp versions is more sensative or less than others and the ones in SUSE / Debian / Gentoo is of the x86 / stable / older versions and you might have the testing unstable version that causes the bug or ~x86 version. See /etc/make.conf / search the forum for dhcp working versions or copy from gentoo install cd /dvd and replace with current SL version to see if this fixes something.
If in the live cd / dvd it gets connected but not the installed then something was messed up during install ?? If yes then the cable / router / pc +SL is good.
If not then cable / router needs attention / 5mins powered off to get rid of static etc and powered back on or even a good reset to default after backing the config file of it up.
Some routers the bug comes back if you reimport the backed up config file = weard but setting the reseted to same settings = working still ?? Linksys firmware aarrgghh.
Alternatively getting the latest firmware for the router or even openwrt linux firmware for it helps to fix this.
Then can you see the router / wifi router and login to it or your cable / modem and login to it but still no inet , if yes = resolv.conf = funky.
If not then likely the "emerge -s dhcp" needs to be checked as it could have the funky one as posted a few times in the forums.
Think the 3.06 and before was okay and 3.10 or later was okay again. In between was funky versions have to check on numbers.
By default my bcm440 lan Dell laptop eth connection connects in all of them provided there is no mac adress block or I am using a good cable as some routers hate patch cables in a cross over port or vica versa something like this and causes timeouts in SL as a result = 169.254..... ip's = bad router firmware.
This is about the extent of the problems.
Listing the dmesg tail part also helps to find what it is complaining about and so can find the bug / cause for this problem. Some one will psot with dmesg tail how-to code to use or search the forums for it.
Hope this helps.