/var/run/mysqld/mysqld.sock

I am not sure why lately ppl define the path to their DB_HOST like you do.
(Assuming it is a way server is configurated (or using a MAC) and/or as pseudo layer of security?)

Anyway, you will have your reason for it, maybe one of these codelines below could help you.

define('DB_HOST', ':/var/run/mysqld/mysqld.sock'); 

I could be wrong but the colon is important with this so try it out.

define('DB_HOST', 'localhost:/var/run/mysqld/mysqld.sock');

Assuming the path is correct you show us.
or maybe some like this?:

define('DB_HOST', '127.0.0.1:10000');
define('DB_PORT', 10000);

Check if it is the correct port else change it into the right portnumber.

Last but not least:

define('DB_HOST', '127.0.0.1');

And like others also may ask, why not using localhost as 90% would/can do?
Hope it helps you to the right direction because this is all I can offer.

note
Not sure if it will show you anything but maybe try following to add in your wp-config.php also.

define( 'WP_DEBUG', true ); // set to false to disable all below
if ( WP_DEBUG ) {
define( 'WP_DEBUG_LOG', true ); // writes errors down in wp-content/debug.log
define( 'WP_DEBUG_DISPLAY', true ); // throws error output on screen, set to false to disable screen output
@ini_set('display_errors',1); // set to zero to disable displaying it and only writing to logfile
define('SAVEQUERIES', true); // could have heavy perfomance impact, set to false if not needed!
}