For anyone that is intrested, I now have the solution:
If Internet Explorer or Firefox is not working, or if you are prompted to login to the Identity Cloaker proxy servers, when Identity Cloaker is not connected, this is very likely because the Identity Cloaker proxy is switched on in Internet Explorer (and possibly Firefox too) still. It is not a common problem as Identity Cloaker should normally disable the proxy automatically when disconnected.
To disable the proxy server in Internet Explorer, please follow these steps:
1) Select Tools => Internet Options.
2) Select the Connections tab.
3) If you are using LAN, click "LAN Settings" button. If you are using Dial-up or Virtual Private Network connection, select necessary connection and click "Settings" button.
4) In the "Proxy Server" area, remove the check mark next to Use a proxy server for ....
5) Click OK.