Internet availability with multiple users sessions

Hello,
The issue is following : a computer with Win7x64 pro is shared between 3 users, each of them having their session. If one is logged on and browses the web and a switch user is done., the second user cannot access the web. Other example if a user browsing leaves the computer for a while, the screen saver logs the session. If another user logs also and attempt to surf the web, the web page is not displayed. What can be the limitation here ? The browser is waterfox, antivirus is mcafeee. THanks for any suggestion

Actually it turned out to be that the computer was running a trial version of McAfee which by simply upgrading to the full version, solved the problem. Thanks for you idea, i wouldn't though to do the test.