if the game has on-line capabilities for anything, updates, online play, or even a spyware app it may have added something that is checking the net everytime you open the browser. first try a spyware scan if you have not already.
http://download.com.com/3000-2094-10...ml?legacy=cnet
if this does not find a problem and fix you up, try uninstalling the game. if the problem still occurs use system restore to go back just before you installed it. if the game is the problem the web site for it may have a patch or if it is a older game that was designed for 98/me you might want to try compatibility mode.