Usually Wi-Fi is a default setting in most computers so you actually need to turn your Wi-Fi off when you're using your ethernet cable because it's supposed to try and keep switching to Wi-Fi.
As for not connecting to the web usually is first priority is to connect you to the Wi-Fi and that's usually what the indicator the bottom is about it's connected to the Wi-Fi not necessarily the web it may be your Wi-Fi unit that's the problem but most likely you bought this from Best Buy so give them a call and ask him that question maybe there is something wrong with it but really usually it's what I just told you