[Black Tiger]

First of all, the index.php is not an address but a file.
I'm trying to understand what you are saying, please tell me if my interpretation is correct.

You have a http://www.yourforums.com domain name. When all is setup correctly on the webserver, automatically the file http://www.yourforums.com/index.php will be loaded and your forums start to work and display fine.

After logging in, you and your users are redirected to the login screen again.
Only if you use the full http://www.yourforums.com/index.php line in your browser, you seen to be able to login fine.

If I understand this correctly, the cause is almost certain a cookie problem and possibly a cookie path setup wrong in your configuration of the admincp.

The best way to fix this is to leave the cookie path in the Admincp standard or put it back what it was. If all is correct only a / (a slash) should be present in that option.
After that close your browser, remove all cookies from your pc so your browser is clean again, and then try to login the "normal" way by only using the .com domain name without the index.php extension behind it.
Things should work fine now.