Sportic internet connectivity issue

Hi. I've been having an issue with my internet for several weeks now that I'm hoping you can help me solve. It will say I am connected, yet I am only able to load a few websites, Google, Facebook, Wikipedia, Youtube etc. Upon checking the status on my connection I noticed that the IPv4 Connectivity reads 'No Internet Access'.

The strange thing is it seem to come and go at random. It will stay for days on end, then be fine for several days, then come back. It's done this about three times now. I've tried several things, but nothing seems to make any difference either way. I've tried resetting the router, replacing the cables, network diagnostics, system restore, changing the proxy settings, the IP settings, the preferred DNS server. I've tried updating and reinstalling the drivers. I've tried several command prompt executions i.e. ipconfig, winsock, chkdsk. Even when I'm in SafeMode, the issue still persists.

The only thing that seemed to make a difference is when I finally tried refreshing my computer. After that, the Ethernet worked perfectly, although the wifi was still out. But as soon as I downloaded and installed the first few windows updates, now the internet does not work at all. Now it says it is limited and the IPv4 and IPv6 both say 'No Internet Access'.

I am rather frustrated at this point, as I still have no idea where the issue is coming from. The only thing I can think of now is that it may be an issue with the modem itself, perhaps it needs to be replace, or maybe a hardware issue with my computer (if that is possible?). It's hard to pinpoint which it might be as, although I have been having issues with several of my devices when it comes to the connectivity, its only on my main computer that it is the most severe and has no access at all currently.

I called my ISP during all of this, but all they seemed interested in doing is selling me a more expensive service package and were reluctant to say it might be a modem problem. I know it's not that other devices are just sucking up the internet, because we have not upped our internet usage in anyway, and even when no other devices are on I am still having the issue with my laptop.

So my questions are, is there anything else I can try that I haven't already? Does it sound like something that would happen when a modem starts failing and should I try replacing it? And is it possible that it might be a hardware issue on my computer that is causing the problem? I have also heard that it might be a Windows 8 issue, but my other laptop also runs on Windows 8 and the internet is working just fine for the most part.

The main computer that is having issues is an HP Pavillion G6 with Windows 8 laptop. My ISP is Xfinity and we have been renting the same modem from them since it was installed two years ago, an Arris TG862G Cable modem.

The computer I am using is about three years old, and the modem is about two years old. Both have been working perfectly together until this started happening.

Any suggestions would be highly appreciated. If you need more info, please feel free ask and I will do my best to answer you as effectively as possible.

Definitely start with the ISP replacing their modem.

Also try connecting a Ethernet cable to the laptop when this problem occurs, see if that works or not.
Another possibility is to replace the built-in wireless card. They are easy to replace and not expensive.
One last possibility is to use a USB wireless dongle instead of the built-in wireless.

Thanks for the reply. Interestingly, the Ethernet cable seems to work some of the time, and other times not. But I will definitely give them a call on Monday and see if they will send out a new modem.