This suggests you have something wrong with any of:
- database name
- database host/server
- security settings on your database
When you created your database, did you grant the user access to the database?
Proper database-configuration includes:
- make a database
- make a user, with password
- grant the user permission to use the database
See this related article for tips: How do I create a MySQL database for Zen Cart?
Specific steps for creating and securing a database on "your" server can be obtained from your hosting company tech support.