If both of your laptops are connected to your router, but one is displaying a "limited access" message, perhaps you should try repairing the connection of that computer, in order to see if you would then be able to access the Internet.
One way that you could go about repairing your connection would be to right-click on the network connection icon for the network that you're connected to and click on the "Diagnose and repair" option, which should run some tests, to see if there is anything wrong with your connection.
Should it turn out that there aren't any problems with your network connection, perhaps you should try disconnecting from your network and then reconnecting, which may help to fix this issue.
If that still doesn't work, another thing you may want to try doing would be to simply restart your computer and then try to connect to the network again.
However, if after you restarted your computer, you are still unable to access your network, perhaps you should try resetting your router or hub by unplugging it for about fifteen seconds or so and then plugging it back in. Then, using your laptop, you should try to reconnect to your network to see if you have a full connection to your network and the Internet.
Good luck and I hope I helped you!