Remote Desktop Connection

I have a desktop PC at home with XP pro. It has a NIC card and a wireless NIC card. It has 2 IP addresses XXX.XXX.0.XX3 and XXX.XXX.0.XX2. I also went to http://whatismyipaddress.com/ and got a different ip with a totally different format XX.XXX.XXX.XXX. When I am at home, and connected to the network there with a win XP home laptop. I can connect to the desktop using Remote Desktop Connection. and XXX.XXX.0.XX3 as the IP.
Here is the problem: When I take my laptop to my office, I can’t connect. I’m pretty sure I need to change the IP. I’m sure its something pretty simple since I have connected at home. Please help, someone.