A better approach might have been to ask what problems can cause Zencart to be unable to find the database.

What point in the installation process are you seeing this error ?

If you are using shared hosting, are you adding your hosting control panel user name to the database name ?

example : if you create a database named zencart and your control panel user name is foobar, you need to tell Zencart the database name is foobar_zencart during the installation process.