Just use another router between the existing router and your computer. If it's a wired connection, use a cable router. Otherwise, if it's wireless, use any router with a wireless facility and is capable of the configuration you want.
A better way, would be to use a managed switch between the existing router and the network. Then you could set up fine grained control as to who can access what. But from your post, it sounds as though that's not an option.