Unable to edit user Profile

In a nutshell, no one is able to edit a created user profile even when logged in as User #1. Permissions to alter the Profile are given to those in the Administrative role. Yet, when someone tries to edit their Profile - or when an Administrator tries - they are always directed to a user login page. This is, I assume, a security measure to confirm they really ARE authorized to edit the user Profile. However, even though the login ID and password are correct everyone is getting an Access Denied message.

I have turned off several of the installed Profile enhancement modules - and removed them - in hopes of discovering what is causing this problem. So far no improvement. Have no idea what could be contributing to this issue so am unsure where it needs to be reported further! This is a rather critical issue as I need to be able to edit Profiles upon registration so as to select roles to establish permissions and for other reasons.