What is wrong with my computer?

[Heybail]

Last night when I got home I turned on my laptop (It's an HP Pavilion dv5-2135dx that I bought in November 2010). When I tried to get on the internet it'll load my homepage but if I try to go any further I'll either get a "Internet Explorer cannot display the webpage" or a screen like the attached picture (depending on the website). There are point where I can get a page to work for a couple minutes but then it goes right back to not working.
Last night I got a notification from Norton Antivirus that my software was out of date, so I updated it and it did some autofix on my internet which fixed it for the rest of the night.
Today when I turned it on, it started doing the same thing with my internet again. I've checked that my internet is on, the wi-fi is on, and the WLAN is on on my computer. Also, I did a scan and I don't have a virus.

Does anyone have an idea what is going on or how I can fix it?

Thank you!
P.S. I don't think it's the internet itself because my mom is having no problems on her desktop and I am still picking up the wi-fi on my cell phone and iPod.