Internet with modem works but wireless router says "local only"

Hi,
I will try to explain my problem that I have a bit better.
I have a Toshiba laptop, 32bit Vista Home Premium.
I have had an internet connection through modem for a while, everything is good. Now I bought a Linksys WRT54G router, to be able to use the laptop with wireless. Did the setup, all was good, then suddenly no more connection.
Tried to reset the modem, the router and restart the laptop, got a connection again, but it went after 5-10 minutes, just simply stopped working. I still am connected, but it says "local only" and once "limited connectivity".
When I then connect the laptop directly to the modem with a cable, I have internet.
So the router seems fine, modem obviously, too.
What could be the problem that it always says "local only" all of a sudden, although I know there is internet???
Thanks for your help...

The router must be given an IP address that's in the same subnet as the modem. So if your modem has an IP address of 192.168.0.1 then your router must have an IP address of 192.168.0.x where x is a number that is outside the range of the modem's DHCP server. 250 works good, so 192.168.0.250 would be entered in the setup screen for the router's IP address. You also want to turn off the routers DHCP server and keep the one on the modem active. The subnet mask should be the same on both devices too, usually 255.255.255.0

Plug the modem into a LAN port, and NOT the WAN port. Power everything down (including the computer) then turn on the router, then modem, then computer and all should be good.