The description of issues could be Internet related and/or resource related with the computer.
Try running a Ping Plot to 206.16.60.38, for a few minutes, after the problems arise and see what the Internet path looks like between you and the servers.
Also try disabling ALL the options in the Options->Graphic Details->Advanced panel. Also make sure the "Maximum Texture Size" in the "Video Options" is set to 1024, or less. See if that clears it up. If it does, then a DXDIAG output would go a long way in helping determine what options should be set and which ones should not be set.