Thanks for your advice. AskApache certainly did do something in the .htaccess file. I removed all the code it added but it did not fix it.
- Replaced the wp-config files with older files
- Replaced the SQL database
- Replaced the .htaccess files
- Deleted the security plug-ins
This situation reminds of when I use to set passwords which were too complex for anybody to remember, in the end I would end up forgetting the password.
There is one thing left to do, which I feel would be inevitable at this stage, and this is to completely replace WP installation and start from the beginning. I will eventually isolate the problem. I feel one of the plug-ins changed the location of the WP-admin and WP-login locations, to an undisclosed URL.
Edit: Found this post - http://wordpress.org/support/topic/askapache-password-protect-problem-1. Seams to be the offending plug-in. I will reset the plug-ins folder and see how it goes.