-EDIT-
What a complete arse I was, just now. I typed this whole reply and forgot to thank you for your reply so far. THANKS!
Well, after wrestling with the case for a while, I managed to plug in a new NIC card. I disabled the onboard NICs in the BIOS and used just the one D-Link card. Things then went the same as before. It worked nicely for a while, then it suddenly stopped paying attention to any/all traffic on that card. I guess that means that it's not a hardware problem... Joy.
The only thing I can think of is relating to the static DNS rules I have set in place. The way I was able to get it to connect to websites when I enabled the secondary NIC was to specify that DNS in both TCP/IP Properties, in addition to the typical 192.168.0.1 that must be there for all domain controllers to function properly.
Also, I clearly cannot release/renew the IP since it's a DC, and has the IP static.
Yes, I have many MANY backups of the data. This is going to replace an existing system, so data loss won't be catastrophic in this stage, just annoying. I'm also going to set up three separate forms of data backup, two of which will be shipped off-site upon completion.
Now, here's where it gets interesting. Even when I try to do a normal system restart once the NIC stops responding, the server hangs on shutdown and requires physically pressing the reset button. Pinging results in 100% loss once the network stops, also. No outbound nor inbound work on the domain NIC.
-Devin