If this is WEP protected that happens a lot. I can't see any router settings in your post or much else so please start with a lot of what we know from the next link.
I also can't find the model number and country to check if it does Netflix.
I have a 46'' samsung LED smartTV that is about 2 years old. I'm trying to connect to the internet so I can set up Netflix for my grandmother. It finds my wi-fi network, and connects to the router, but cannot establish a connection to the internet. it says "wireless connection completed, but internet connection failed". Then it says "check DNS setting from network setting". Where do I do that and what do I need to check? I have a netgear N300 wireless router. Please help, this is driving me crazy