Does your internet connection work properly? You can check this by using ping to see if you can reach other computers on the internet.
For example "ping www.linuxquestions.org
If you don't get replies you can use the IP adres:
If you get replies now you should add the nameservers of your ISP in /etc/resolv.conf. Those servers will convert the name www.linuxquestions.org
to its IP adres so that your computer can commnicate with it. Your computer only communicates with IP adresses. It needs those nameservers (DNS servers) to recognice names on the internet.
Your pc uses the names of the gentoo mirrors to find those mirrors, but it won't reach them if /etc/resolv.conf is empty so it doesn't know their IP adresses.
If this doesn't help what kind of errors do you get? Maybe try mirrorselect to automaticly select some mirrors where you can download from. It is mentioned in the manual.
You can also try the command "ifconfig" to see the settings of your network cards.