No one here is giving you 'the royal runaround" as far as I can tell. You were advised correctly that your hosting providers would be able to help you with your database name, database user name and database username's password. There is no way that anyone here can know that information.
Your posts also are being read carefully.
Regardless of whatever other connection files you have on your server, the URSP pages refer to the localhost.php connection file, so it is this one that we should be concentrating on. You can use the same database as your other connection file (as long as it doesn't already contain a pre-existing 'users' table), and you will use the username and password that your hosting service provided you with.
As your existing membership database has the same user name, user password, and database name - and was presumably connecting OK before you began installation of the URSP (or wasn't it?) - then the information for the localhost.php connection - if entered correctly - should connect OK too.
If you have been following the directions, you will have created a new table in that database (users) using the 'users.sql' sql from the 'Database' folder in your URSP soultion pack.
The two links provided in your post, (www.gcssepm.org/users_LogIn.php & www.gcssepm.org/users_confirm.php) seem to be indicating that the user name in your localhost.php file is still 'root', with no password set. This needs to be checked and corrected if so.
Update your localhost.php file in the Connections folder, check that the info entered into the WA_Globals.php is correct, and upload all the URSP files and folders (maintaining the structure of files and folders) to your remote server. Ensure that the table 'users' exists in your database.
Post back with how you get on.
Edit: I checked back through your other thread with Jason, and notice you have changed some of the require_once calls to point to the other connection file. Please could you replace those pages with fresh original pages that refer to the original connection folder:
That way we know where you are. It is also likely that your existing 'membership' connection file uses different variable names to represent the connection details from the ones that URSP uses. Just do the localhost.php file and the globals file and upload the entire contents of the URSP to your remote server. Don't change any paths just now.