It is normal for your IP address and default gateway to be different!
From what you described I am almost positive that your firewall settings are causing the problem. I'd make sure that both your Norton Firewall and Windows Firewall are off. Your router and modem have built in firewalls which should protect you from most threats. The most common issue computers face is spyware (somewhere around 90% are infected), but thats a whole other story.
Click Start
Go to Control Panel (or settings > Control panel)
Double click windows firewall
Make sure it is set to off
I'm not 100% sure on Norton but try
-Double Clicking the Norton Icon
-Look for "configure" or "settings" and select that
-You will have to permanently turn off the firewall, usually Norton will turn it back on in an hour or until you restart.
Let me know if that helps!