What if your iPod touch connects to your network with a stable connection and the ip address and dns cache stuff still doesn't auto fill out?

It is probable that the network that you are connectiong to does not use a DHCP server, meaning that each computer sets its own IP and DNS servers, rather than being assigned one by a DHCP server. Most routers serve as the DHCP servers for their network(especially in home networks). If you know the DNS servers that you use elsewhere, manually assign them in the iPod, and try to find the router's ip and use the first three sections of it and then add your own number(greater than zero but less than 255, 1-10 are your best bets though) as the last section.