Network Without Internet

[Moe]

For the one computer in question you have to manually address it.

Give it an IP address and subnet mask matching the rest of the network but outside of the DHCP pool and leave the gateway or router address empty.

Without a gateway or router address, it doesn't know where to send packets addressed outside of the local network so it will be impossible to reach the internet.

[RobertX]

Wow, that advice actually worked; my head was truly up my ass on that one.

Thanks!