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Sometimes, the Wi-Fire Connection Manager reports a successful connection a few seconds before the connection has actually been established.  Wait a bit, and try to open your website again.

Should the problem persist, it is likely caused by a failure of the Macintosh to receive a valid IP address from your wireless network.  If this occurs, try to connect again by double clicking on your target network, and verifying that your security settings are properly configured (if it’s a secure network).

If you continue to not be able to open a website or generally be online, please verify the IP address by going to Network Settings, and select Ethernet Adapter (en2) [Note: it may be en3 or another number, depending on your computer.] from the Show drop-down menu.  If you have an IPv4 address that starts with 169.154., then you have a bad IP address. (Please note that if you have a number other than that, you are successfully connected to the wireless router, and the problem is on the wireless router’s connection to the Internet).

However, if you have a bad IP address, please select Network Port Configurations from the ‘Show’ drop-down menu. Then uncheck Ethernet Adapter (en2), and click Apply Now.  Wait a few seconds, then recheck Ethernet Adapter (en2), and then click Apply Now again.
Now select Ethernet Adapter (en2) again from the ‘Show’ drop-down menu, and then click on the button Renew DHCP Lease. 
If a new IPv4 address doesn’t appear within several minutes, then go back to the Wi-Fire Connection Manager, disconnect from your target network (if it reports you are connected) by double clicking on a different network, and then attempt to reconnect again. 
Alternatively, if this occurrence repeats itself, reboot your computer.
Note: These symptoms can also happen when the router is not set to automatically assign IP addresses, or if the router itself is not on the Internet. In these cases, ask your network administrator for assistance.