Stumped: Database connection error.

I am relatively new to php and mysql, but overall a (hopefully) generally competent unix admin.

I have created a wordpress user and database in mysql with the mysql command-line client, and
using the directions in the mysql documentation.
I have set the password for the wordpress database user. I have confirmed, using the mysql command-line
client, that the ‘wordpress’ mysql user can get in
using the password I created, and that there is a
‘wordpress’ database table set up.

I have also verified that the entries at the top of
wp-config.php are set correctly. (I’ve gone so far
as to cut and paste these values into the mysql
command-line client to confirm there were no typoe, and that I could log in using these values.)

After all this, though, I still get the generic
‘Error establishing a database connection.’ I do know that mysql is indeed running. I checked the apache logs, and there are no errors –
the php pages are getting served just fine. I tried
to do some sleuthing, as I wanted to know whether or
not MySQL was actually seeing connection. Unfortunately, after hunting around the filesystem
(as root) and looking through MySQL docs, I couldn’t
readily find a source of info about successful and failed login / connection attempts that MySQL had seen.

Can someone help guide me in the next steps of the problem-solving process? I”m rather stumped from here. I’m guessing it’d be helpful to know if
MySQL even sees the connection attempts, but I don’t
know how to find / extract those logs.

Thanks!
– Larry