Do you have any other device which is connected to the same router through wireless? If yes, you may then try disabling that device and then as it can be a duplicate IP address issue.
If the internet connection is fine then a basic restart of all these devices one by one starting with the router should fix the issue.
Else the issue can be with the username or password or with the Playbook's WiFi option itself. In the last case you may need to contact the RIM support.
