The router (assuming it's working) should just see the net connection as a network to which it can connect. It should see no details beyond that.
I'd try a "factory reset" to see whether the configuration had somehow got screwed up. If that doesn't work, then I'd begin to suspect that the hardware had developed a fault. Seven years is pretty good going for modern plastic appliances. Stuff ain't built to last these days.
Interesting. I've never heard of Tomato before. Looks like it puts the software on most routers to shame. I wonder if the QoS on that is effective. I've never seen an improvement using QoS on several devices before now.
I have just pulled this router off the scrap heap and had the same issue.
It appears to be a problem with the router's DNS look-up, try setting your computer's DNS servers manually (I use Google 126.96.36.199 188.8.131.52 but your ISPs should work as well). You should set this on your computer so that the router does not do the DNS lookup.