Windows 7: Internet Connection is fine and strong, but cannot connect to internet

Yesterday, I left my laptop on and walked out of the room for a few minutes. When I came back, it had spontaneously restarted and after that I turned it off. When I came back a few hours later, the screen said that the computer could not boot up, and then I commenced with start-up repair:




After it finished, I rebooted the computer and everything was seemingly working fine except that I couldn't get into firefox. Whenever I would click the little icon on the bottom of my screen, nothing would come up. So, I decided to try getting on internet explorer, and I could pull up that window, but it came up saying that "Internet Explorer cannot display the webpage." So, I clicked on the button that says "Diagnose Connection Problems" and it went to the troubleshooter, which resulted in "The remote device or resource won't accept the connection." (I'm using a wireless connection)

But, when I troubleshoot outside of internet explorer (right-clicking the internet access button on the bottom of the screen) it says there is no problem because the internet connection is fine.

I've tried, of course, restarting the computer and a system restore but those didn't fix the problem.

If you have any solutions to the problem I would be very thankful. If not, should I just take it in to be looked at?