Do you have some VPN client installed? Or some other antivirus together with installed Parallels Internet Security? There could be a conflict between Parallels Internet Security (Kaspersky 2009) and VPN client/another antivirus. It is not a well research issue for now.. Please try to remove Kaspersky 2009 and reboot the machine.
If you don't have any VPN client or firewall, Right-click "My Computer" -> "Manage" -> "Device Manager", unfold the "Network Adapters" and send a problem report using menu of Parallels Desktop "Help"->"Report a Problem" and post here the report ID.
If after uninstall of PIS and reboot the network will continue not function, but there will be some adapters in the ipconfig /all output,
Code:
click "Start" -> "Run" and execute cmd.exe. Type in the appeared window two commands (without quotes):
netsh interface ip reset resetlog.txt
netsh winsock reset