What version of Windows is installed on the computer? What version of McAfee's software is installed and do you have an online account at the McAfee website or did the McAfee software came with the computer?
Did you check with this article: Required Reading - Home User Assistance Malware Troubleshooting
Are you able to access the Windows Update website here: http://windowsupdate.microsoft.com
I am having exactly the same problem. Will connect to my home network but not the internet. Take forever to shut down computer for a reboot. Has anyone solved this problem yet?