Ok, thank you for answering the questions. Lets take a look at what they tell us and see if we can come up with any ideas.
1 - the fact that ping does not work indicates that there is a problem with the IP sng dutack or something is interfering with (possibly blocking) communications. Ping uses raw sockets so it bypasses TCP and UDP and operates on a lower level. This tells us that the problem may be at a low level.
2 - The fact that other devices on the segment work in both directions along with the other steps taken suggests that the problem is localized to the DNS server. Specifically that you have changed ports on the switch, changed the cables, etc.
3,7,8 - Showing zero errors is a pretty good indication that you don't have a conflict, a jabbering device, or an overloaded segment. It may also indicate that when the server does go down, that it has a broken connection to the higher level applications that would notice the error.
4 - Ethernet lights blinking indicates that the card appears to be functional at a low level. It is detecting connectivity and the data carrier.
5 and 6 - rebooting not solving the problem says that it isn't caused by a software lockup. You either have a physical problem where something remains failed for a period of time or a configuration error that persists through reboots.
9 - this one is telling. You moved the configuration to an otherwise working server and it too starts giving you trouble. This is a strong indication that there is something in your configuration that is causing the network to stop functioning.
I think the problem is localized to the servers. There are still several things that could be the trouble, but at least I think you know where to look. Here would be the next steps I would take:
1 - can the server 'ping' itself at the local host address of 127.0.0.1?
2 - Are you running any sort of firewall, such as IP tables, or other "security" program with a dynamic response such as denyhosts?
2A - if you are running any such application, get a listing of what its state is. Perform a command such as iptables -L to list the status.
3 - does ifconfig show an IP address being assigned?
4 - if you run ifconfig a couple of times, does either the Rx or Tx packet count increase?
5 - look in the syslog and see if you have any errors. Dmesg could also be of value, but it is more difficult to interpret.
When you do ping to or from the DNS server, what error message do you receive? See the following:
http://www.chicagotech.net/troubleshootingping.htm It contains some of the common error messages along with what they mean.
6 - use the netstat and see what ports are open. Specifically does port 53 have anything listening on it?
7 - if you try to ping 'google.com' what error message do you get? Is it different than trying to ping a local address? Again, check what the error message indicates.