bad network adapter takes down entire network?

This is the problem with basic switches, if it had been something like a cisco catalyst or an HP procurve it may have detected erratic activity on the port and shut it down, this would of course have meant you'd have no DNS if you only have one DC, and no way for users to log in, but the network would at least be effectively "up". My advice is to invest in a couple of 24 port procurve switches and give them a basic configuration, then team the NICs from your DCs and the like so that, should it happen again, the switch will shut down the faulty port.

With regards to troubleshooting the existing NIC if it's faulty hardware who knows what it's spewing out in to your network, maybe if you download something like wireshark and have it running on a client PC when you plug the other NIC back in you can see what traffic it's creating or where your packets are going. Also to test if it's a hardware or software issue you could try a linux live cd such as Ubuntu 10.10. If you load this in to RAM and test the NIC (live cds do not touch the HD so are safe to run for hardware diagnostics) you'll be able to see if it's software (your installation of windows) or hardware.

If you want to troubleshoot it in a more "constrained" environment, hook it up to another machine running Wireshark or similar with a crossover cable. That way you're not risking your network.