I'm having problems with connecting on my laptop (to the Internet )?

So, on my laptop (which I keep very clear of any viruses by the way) I can't connect to any websites besides Gmail. I don't know why this is, since it is connected to wifi. I have windows 7 on a very new laptop (only been around a few months). When I try to connect it brings up "Internet explorer cannot displaythe webpage." and when I click on the troubleshooter it tells me "the remote device resource won't accept the connection." it's telling me that tha means the webpage isnt set up to receive signals? So basically, every webpage i tryis not able to recieve signals from me except gmail. I have tried restarting the computer (which only works for about fifteen minutes before it goes back to not working), I have tried disconnecting and reconnecting to the wifi, disconnecting the power cable to the router and reconnecting it about 30 seconds later. None of this works. Also, every once In a while a "backdoor" virus shows up in windows defender. I keep getting rid of it and reappears. It hasn't shown up in a bit, but it keeps coming back. Does this have anything to do with it? I have webroot security software, and it works quite well. I keep scanning and it keeps coming up with nothing. Any suggestions? Sorry for the long explanation. and any weird errors that might be going on in it, I'm on my iPod and it always changes things oddly (also it's hard to type). Anyway, if you can help me thank you so much!! Please, I really want to be able to use my Internet on my laptop again. Any thoughts on the weird virus thing btw? Thank you!!