Are you saying that the system exhibits...no other problems?
Only when you try to access the Internet?
Let's try this.
Download/install BlueScreenView, http://www.nirsoft.net/utils/blue_screen_view.html
Double-click BlueScreenView.exe file.
When scanning is done, click Edit/Select All
...then File/Save Selected Items
.Save the report as BSOD.txt
.Open BSOD.txt in Notepad, copy all content and paste it into your next reply