Dakota - I just set up my first MySQL database and was having the same problem. I did as Peter suggested and it worked. Of course, using your cpanel log-in is not the final answer.
Here's what I found. It's fundamental and probably available in the documentation but as you said, some of us learn by doing.
You set up users in the MySQL maintenance section (second section). What I discovered is that you then need to go into the top section and select that user and select add user to database. Now it works as it should.
Hope this helps.
