I think the modem has the MAC address of his old computer recorded. Sometime unplugging and plugging the power for the modem can clear this so he can use his new PC.
And you can't disable DNS, if you look in Control Panel>Network Connection, you'll find your Local Area Connection, right click and select Properties, double click TCP/IP.
You need a DNS server, I believe disable DNS on 95/98 is actually the same feature on XP call "Obtain DNS server automatically"