Things to check
I would check MySQL account privilege. Does the MySQL user account has proper write privilege to access the database? Here I'm talking about MySQL user name and password, not CMS admin login and password.
In my case I've always used the root account and never bothered with multiple users for a single database so it's never been an issue. In rental server situation, though, they usually give you a way to set up multiple users for a single database with multiple privilege levels.
I would also make sure you set up a new blank database every time you create a new site. You can do that via PhpMyAdmin.
