My Computer Drops The Internet Connection

I've been having this problem since I bought this new computer a few weeks ago. It's a HP desktop, the model number is s5229uk and it's Windows 7 Home Premium.

At random times when I'm browsing the internet, sometimes it can be every 10/15 minutes, sometimes just a few times a day it will stop loading and a yellow triangle with an exclamation mark will appear on the connection icon in the bottom right hand corner.

I cannot troubleshoot the problems or open up the network and sharing centre because it either doesn't load at all or freezes, and the only way to reconnect is to hold down the power button as shutting down or restarting fails after about 20 minutes of the shutting down screen.

It's more annoying than anything. I've checked for viruses but nothing came up and the one time it's let me troubleshoot, it's told me to reset the router which I did and it didn't work. I thought it might be a compatibility issue with the router (we use Sky) but some days it works for longer than others.

On the Norton internet history for firewalls and connections I found this which I think might have something to do with it. Does anyone have any ideas how to stop the internet from cutting off because me and my Dad are at a loss, and he's quite good at computers.

Another thing is that it won't let me create a system image by backing it up onto an external hard drive, it gets to a certain point and gives me this message: 'The system cannot find the file specified. (0x80070002) I've tried again and it still doesn't work.