Why are you using the control panel/network connections to get connected? Once connected to a LAN you stay connected. And the green light tells you that you are connected.
I think that your TCP/IP settings are wrong, specially now you changed the router. Find in your PC, the properties of 'IP protocol v4' and make sure that Automatic is chosen for obtaining an IP address and DNS server. I am not on an XP machine and not on an English version so I am not sure how to find it, may be typing 'tcpip settings' in help will help.... Sorry for that.