Did you ensure that you added the user to the database? You would create the database in Cpanel in MySQL databases, then create the user, then add the user to the database. If you only did 2 steps (and they are 3 separate steps), then you haven't added the user and need to do so. Click add user after selecting the database and the user in the drop down right beneath the database section. After the user is added, there will be connection strings to Perl/cgi, php, and java.
Next, if you did add the user and it isn't working, what exact error are you receiving. The error is an indication of the issue occurring.
Another point would be what exact program are you using to connect? Each program is slightly different and this is useful to know if you want someone to troubleshoot the issue.
Next, has your domain propagated? If it hasn't, you can't connect using it. You would need to use server.lunarpages.com where server is your server's name like galaxy.lunarpages.com or danzig.lunarpages.com, etc.
Finally, provide the exact settings you are using to connect for the fields that Anthony provided (other than your password). If you want me to test connecting, PM me your password. I can only do the testing, however, once all conditions above are answered and met, since I need the information for any testing.