could be any of the IP addresses listed by several other folks in this thread and then some, but it is most likely 192.168.1.1 which as far as I know is the default IP for LinkSys routers. You might try doing a ipconfig at a command prompt. If you're getting any signal at all this will tell you for sure what your Default Gateway is which is also happens to be the IP address for your router.

It sounds to me like your modem is fine since you can get your Internet going by taking the router out of the picture and hooking directly to your modem. Makes me wonder if the router configuration has become corrupted or someone has hacked in and changed your settings if you didn't have security enabled. You should be able to go back to the original default settings by pressing and holding the reset button on the back of the router for 30 seconds. You will then need to have a computer hooked directly to the router via a Ethernet cable because the reset will in all likelihood blow away your wireless security settings.

If none of that helps; here is a link to LinkSys' support message board which you might look over. You can be certain that if you're having a problem with this particular router there are others who have had the same problem.

http://forums.linksysbycisco.com/linksys/board?board.id=Wireless_Routers

Hope this helps.

Cheers!
Bill