There's at least one former (extremely knowledgeable) @Home tech who hangs in the "Networking" forum, so you might want to try there in the future.
The modem doesn't really require the computer to operate - which is why people use routers and other devices. It sounds like it's working fine. All you probably need is for your computer to know the settings that they are using.
There's really only one piece of information that is essential on my @Home connection and that is my machine ID. You can find this by right-clicking in the background on Network Neighborhood and choosing properties. There should be an ID tag up at the top. Select that and you should be some funky name like "n121932c-a" (totally made-up number) under computer name. There are other settings required, but Windows automatically defaults to the rest. If your network settings are at the default, then the ID should be the only thing you should have to set to be up and running. It's definitely worth writing it down.
Since it's running now, I personally I think it's worth running "winipcfg" from the command prompt, choosing the LAN adapter from the list, choosing "More Info>>>", and writing down all the information that's there. It helps for debugging problems.
Edit: Argh. Beaten by 2 mins. <sigh>
Actually, DHCP should take care of all the DNS and other settings. As long as it's set to "Obtain IP address automatically" under Address, everything else should take of itself - assuming Omaha's @Home is using DHCP.. which I'd bet money they are.