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WiFi Direct is some thing else, you need to run Wireless option in network setup to establish wifi connection with router for internet.
Please go to the Network Settings screen (Network > Network Settings).
Select Start. The network function searches for available wireless networks. When done, it displays a list of the available networks. In the list of networks, select a network you want to connect to, and then select Next. If the wireless router is set to Hidden (Invisible), you have to select Add Network and enter the correct Network Name (SSID) and Security Key to establish the connection. When done, select Next if you entered a Security Key or WPS PIN if you entered a PIN. The network connection screen appears and the verification process starts.
When the connection has been verified, the "You are connected to the Internet. If you have any problems using online services, please contact your Internet Service Provider." message appears. Select OK.
Please reply back with the result.
I understand that you believe TV is connected but error message shown on TV says it is not connected.
Have you tired the suggestion mentioned in previous reply to connect the TV to wifi?