I had the same problem. Mine turned out to be a network security issue. I was so sure it was the note, but I was mistaken.
Do you have the home router secured with a password? Mine is open. The reason my phone wouldn't gain Internet access was because WPS was enabled on an unsecured network. When I disabled WPS entirely it worked.
Try to set it up as unsecured with WPS completely disabled and see if it works anyway. If so, it tells you the problem is in the router settings.
Sent from my SGH-I317 using Android Central Forums
The Linksys WRT330n is secured by a password. The hard part is the history of the phones I had. The OneX had and still has horrible wifi radio issues. It was replced by HTC. Same thing on #2.
I spoke to Linksys several weeks ago. The router is 5-6 years old if not older at this point. They said there is no update for the ????? (Forgot what she called it) said its their legacy router.
If I go to a website.. the green bar will periodically move a litlle stop, move a little and then totally stops. If I reset the router (power) it will work fine for a short period of time and then the lag, freezing starts over again , (browser) and the no connection warnings start again. If you hit try again it usually works. It has to be how the router is communicating with the GN2.
Whats really funny is here I am sitting in Starbucks plinking away at this enote to you and you know how crappy wifi is at Starbucks... Damned GN2 is performing like a Raptor Fighter! Unbelievable!