BSOD Accessing internet

Hi
I have recently wiped my laptop and have very little installed. For some reason after updating windows I keep getting BSOD occurring when I access the internet with both Chrome and Opera.

I had this problem a week ago after installing Windows 7 Ultimate with both 32bit and 64bit and this was after using Windows Update which actually worked at that time. Since then I have rewiped my laptop after learning that the product key was illegal.
I acquired an OEM disc and rewiped my laptop and used the Windows 7 Home Premium key that came on my laptop. I was unable to use Windows Update as I'm sure readers of this will know about the recent convenience rollup updater which has stopped Windows Update working. I have since used wsusoffline tool to update windows to the point where Windows Update then worked again. However since getting my computer completely up to date I have had BSOD errors. I have tried restoring my system to before the recent updates from Windows Update were installed and it has not solved the problem, despite the system not seeming to have this problem before updating windows (though that said I wasn't using the internet much and was just trying to update windows as much as possible before putting other stuff on it).

BSOD just seems to occur randomly (ie with no particular website) and happens soon after I go online in either browser. I have ran Chrome's Clean Up tool and this hasn't fixed anything.
Once I noticed that my graphics card stopped working and after trying to access any latest drivers via nvidia's website and being told to install java I have been unable to as get errors with that.
This is exactly the same thing that happened before.
I have also ran chkdsk etc in the past and no errors were found.
As said I've installed very little other than kaspersky internet security and not put any other software on so am sure it's not malware etc.

Any help is much appreciated!