I am a recent joiner to all things Raspberry and this new fangled Debian thing. So I suspect the technical answers are going to come from Grumpy or Rattus.
The photo of your screen, shows that the ethernet interface has had some input and output, because TX Bytes and RX Bytes are not zero. I.e. The RPi has been talking to something. However, under the that says "eth0 Link encap:Ethernet HWaddr...." I would expect to see a line that says something like "inet addr:192.168.100.nn Bcast:192.168.100.254 Mask:255.255.255.0"
DHCP : Domain Host Configuration Protocol, is the process by which a computer joining a network, makes a request on the network for a network address to be given to it. This would normally be handled by your broadband router. This exchange, doesn't require an assigned IP address to work, and might explain the small amount of network traffic that has occurred. My supposition was that for some reason your RPi wasn't given an address, hence no address given in ifconfig, and the subsequent non functioning of the network connection.