Networked or not? Help

OK guys, here's one to laugh about. I'm not computer literate so please bare with me. I'm running xp, amd athlon, ethernet connection to a dsl router. There is another computer on the premises but I do not want to be networked with that computer but we both share the same router.(SBC 2wire). How can I tell if my computer has been networked anyway. I have Sygate and have seen requests on both computers asking for permission to each respective ip address (static I guess) to grant permission to access. What does this mean. I need to know if my computer has been shanghai'ed against my will. Please help.

 

The Router is a combo Router (from the Internet side), and a Switch the LAN side.

So when you plug two computers to the Switch you have a Network.

However if you are Not giving permission to Share there would not be Sharing.

If you want even more security Unbind the TCP/IP from the File Sharing.

http://www.ezlan.net/network/XP_Net_advance.jpg