If "ifconfig eth0" returns " ERROR while getting interface flags: No such
device" then your NIC is probably bad as Darrin described.

If you instead get something like:

eth1      Link encap:Ethernet  HWaddr 00:19:DE:07:BB:AA
          UP BROADCAST MULTICAST  MTU:1500  Metric:1
          RX packets:0 errors:0 dropped:82374 overruns:0 frame:0
          TX packets:0 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000
          RX bytes:0 (0.0 b)  TX bytes:1728 (1.6 KiB)
          Interrupt:17 Base address:0xc000 Memory:dcfff000-dcffffff


Then I'm guessing your DHCP server has crapped out. If it is your FW/Router,
simply power cycling it my solve the situation. If not, try adding a static
IP and bringing the device up.

vi /etc/network/interfaces

change the line from

iface eth0 inet dhcp

to

iface eth0 inet static
address 192.168.1.20 <-- adjust this as appropriate for your network
gateway 192.168.1.1
netmask 255.255.255.0

and then do /etc/init.d/networking restart

or

ifconfig eth0 down
ifconfig eth0 up

and then see if you have connectivity. If not, my money is on a bad cable or
swtich port.

Cheers.