Any linux that is running a dhcp client (there are a few) should pick up an IP address from your router. The only catch is that it should first have the correct drivers for its wired/wireless NIC.
So, starting from the top let's look if the correct drivers are running:
lspci -k
and look for your NIC cards in there.
Then let's see if the devices are configured, are activated and get connected:
ifconfig -a
You may need to run the above with sudo or su to root first.