[Most of this answer is outdated and will not be useful with versions of Raspbian beyond the first one, "jessie".]
If all the ethernet lights are on when the cable is in, and you can connect a monitor and keyboard or a serial line as John suggests, you should be able to get the connection up.
First, just run
ifconfig. Possibly eth is not up, and you will just see:
lo Link encap:Local Loopback
inet addr:127.0.0.1 Mask:255.0.0.0
UP LOOPBACK RUNNING
You may also see
eth0 listed. If not, don't worry about it for the moment; before doing anything else, it might be worthwhile disabling the network automation since obviously that's not working for you:
sudo service networking stop
sudo service ifplugd stop
These will start again next boot/runlevel change. If you don't want the services to start again at boot, use
disable instead of
stop, in which case you will have to make your own arrangements or do all this manually every time. The second one (ifplugd) is supposed to raise a connection whenever an ethernet cable is inserted.1
Now that's out of the way, if you did not see
eth0 listed earlier,
sudo ifconfig eth0 up, otherwise just
ifconfig again to make sure it is still up. Next,
sudo dhclient -r which should stop any running instances; to be sure,
sudo killall -9 dhclient then
ps -A | grep dhc to check for other dhcp client software, since I think debian uses
dhcpcd (instead of
dhclient) by default. If so, you need to kill that off. Beware that if you have not disabled the networking service as above, it will probably keep coming back.
Once that's done, you should be able to get connected with
sudo dhclient -v eth0. If that doesn't work, add the output to your question.
1. Which may not be desirable for everyone. It seemed to be very pernicious to me even when the service was supposedly stopped, and I uninstalled it with
sudo apt-get remove ifplugd.