If the user has Account Status: Live or Flagged then Capitan will allow them to login, provided their login credentials are correct.
"Email or Password incorrect" means the login details have been entered incorrectly.
Users often copy/paste passwords without realising that they've copied an extra space at the start or end of the password which makes it incorrect. Or they'll make a typo in their username or password. If the user is adamant they can't get in you can
- Verify the credentials yourself by trying to login with their username/password
- Ask them to request a password reset and follow the instructions in the email which comes out (if they don't see it in their inbox check the spam folder)
"Access Denied. Please check your credentials and try again" means the users login details were ok but they don't have the necessary access settings to reach the desired content. This could mean that they aren't in the right Access Group or the right kind of Primary Relationship type - depending on the access restrictions you've placed on the private content.