I'm having the exact same problem. I use a TP-link powerline adapter. It'll be fine for a few minutes, but then it will just stop working. Says in the taskbar I do have an internet connecion, while I can access no websites etc. Fun thing: when I am connected to skype/similar-programs etc I CAN still chat, even though I can access no webpages.
If I disable the LAN adapter and then re-enable it, it'll work again. For another couple of minutes, until it fails again.