This really is completely off topic here.
You would want to not run the DHCP server on the server 2003. I haven't
done this with Windows Server 2003, but I have done it with a Windows Server
2000 machine--shouldn't be a problem. Set the server up with a fixed IP
outside the range given out by the Linksys (or set up as an exclusion)-- On
the Linksys, set up the Server 2003 machine as one DNS server, probably with
the ISP's DNS as another--make sure the clients get both.
I think that's what is needed--but you should be asking in a server-related
group.