First, power-cycle your network. Unplug the LAN adapter from the TV, unplug your router from its power source, then unplug your modem. Let all devices remain unplugged for about a minute. Bring the network up in reverse order; plug in the modem and let it come all the way up, then do the same with the router. When these devices are up and running, plug the LAN adapter back into the TV. Again, let everything sit for about a minute.
Once this is done, go through the connection steps again and when you select the Access Point, make sure to check how many bars of signal strength are colored in on your network. You need 3 or more bars for a stable connection.
The security key is case sensitive so you must type it in exactly as it is in your network information, remembering to shift between upper-case and lower-case letters if it contains letters.
If it does not connect run the Network Test again and post where you are failing. It could be security on your router.
Hope this helps. Good luck!