Okay, I looked through the firewall rules, but I couldn't find anything to help. I have since upgraded to ESET smartsecurity 7, and I also turned off my NAS. When I turned it back on, this time there was a popup about blocking duplicate IPs, but this time I had the option to stop blocking it. That created an IDS exception, which I can see in the advanced settings.
The only problem now is that it is detecting another duplicate IP. This one I can see is the one for my actual computer, attached to the router via ethernet. I don't know what the other one is, and I can only see one in the DHCP client table. I can obviously access the internet, even though my computer is theoretically blocked. I don't know, it's weird.