Unable to login as user in my drupal 6.x website while able to access without login
As you can not login from in your site the only way to do something is from database end, if you have access to database try doing this to come out of this mess up:

Try to empty the sessions and the cache tables. Not DELETE! Empty them.
then see if you can login from http://www.yoursite.com/?q=user

Or look if your site is in maintenance mode if it is the follow instructions given here: https://www.drupal.org/node/276457

Hope above will work for you and you will get your site back to normal.
Good luck!