I have already spent several days attempting to install Moodle 2.4.1 on a local computer running CentOS 5.8, with PHP Version 5.3.3
I am facing the same problem, the installation doesn't progress after the database connection; it outputs the same error message:
PHP has not been properly configured with the MySQLi extension so that it can communicate with MySQL.
I've tried so many things...
First thought it might be a difficulty related to Moodle version, so I tried with Moodle 2.2 and even with Moodle 1.9.9, always with the same problem.
Then I thought that maybe using PostgreSQL it would be alright, but nope... same problem! (just a minor change in the error message)
I have visited forum threads and tried many of the recommended solutions that have worked for others, with no success for me!
I have edited the PHP.INI file to add the extensions, no success.
Something interesting, it seems that the mysqli.dll file is not present in my computer. I tried downloading it and then putting it where I assumed it should be, but it didn't work either.
One of the last threads suggested editing the mysql.ini and mysqli.ini files... to my surprise, I searched for those files and also discovered that they are not present in my computer either.
Nevertheless, I have indeed installed mysql and mysql-server. I also installed postgre and postgre-server... how could it be, that there isn't a mysql.ini of mysqli.ini file in my computer?
Some other thread suggested using the ./configure command to recompile PHP, but maybe that wasn't CentOS... I haven't been able to use such command, the system indicates that it doesn't exist.
So, by this time...
I'm desperate !!! PLEASE HELP !!! PLEASE !!!
Maybe Ken in his wonderful spirit of sharing might be able to help me, I can see that the solutions he suggested have indeed helped other people with the same issue...