Server had a power failure, and when it came back up the network will not function. Here are the symptoms:

NIC has link light
I can ping my address and the loopback
I can not ping any other addresses, not even the local gateway
Network equipment has been verified (it did not suffer a power loss)
ifconfig shows the nic UP and with an IP, but the RUNNING portion is missing (see below). I have restarted services, verified config files, etc. Please let me know if you can assist - and thank you!

eth0 Link encap:Ethernet HWaddr 00:50:56:BE:00:31
inet addr:<removed> Bcast:<removed> Mask:255.255.255.0
inet6 addr: fe80::250:56ff:febe:31/64 Scope:Link
UP BROADCAST MULTICAST MTU:1500 Metric:1

I ended up fixing it - here was the solution. I put my laptop on the network cable from the server, and gave it the same IP and verified the network was operating normally. To me that narrowed it down to a driver or hardware issue. Given the recent power disruption, I decided to take the hard disks out of the server and move them to an identical spare chassis I had in storage (the NIC's for this model are on board). I moved the RAM as well, fired up the server, and the network was working again. Safe to assume something in the power loss caused a hardware issue.

Well done.

FYI pinging localhost or your own IP address does not actually use any real network hardware. I've also had network adapters fail in a similar manner.