Impossible to connect locally to Mysql

[Arnaud Forster]

Hello all,
I've installed the last Mysql Version on a new Centos system. Installation was sucessfull and I can connect to mysql from the command line (mysql -u root -p xxxx), I changed the initial password of the root account and created a new account for my new web software.
Finally I installed phpmyadmin to be able to have a look on what's happend in my system.

My firewall is off and scelinux is disabled.

The mysql hostname is define as follows :
mysql> SHOW VARIABLES WHERE Variable_name = 'hostname';
+---------------+-------------------+
| Variable_name | Value |
+---------------+-------------------+
| hostname | support.gfb.local |
+---------------+-------------------+
1 row in set (0.03 sec)

With phpmyadmin, impossible to get a connexion to my database server (on the same host) and the new software I'm trying to install can't connect to. It seems Mysql is refusing connexion from localhost (i tried with 127.0.0.1, too) ...
I already spent hours but .. doesnt know what to change ...

when trying to connect with phpmyadmin, I get the following message : connexion to server MySQL not allowed.
When trying with the software I shoud install, I've to enter the name of the server ( I tried localhost and 127.0.0.1) , port number (defaut 3306) and a user and password. With the user I'm trying, I can connect from the commmand line. When trying during the installation, I get the following error : Could not connect to database.

Finally I checked to see if Mysql is listenning :
tcp 0 0 127.0.0.1:3306 0.0.0.0:* LISTEN 16749/mysqld
tcp6 0 0 :::33060 :::* LISTEN 16749/mysqld

wich seems fine ... so.... what could be wrong ?? If someone has an idea, it's very welcome :)
Per advance, thanks to all for your help :)