Since you do have ftp access, edit your wp-config.php add these lines:
@ini_set('display_errors',0);
define('WP_DEBUG', true); // Turn debugging ON
define('WP_DEBUG_DISPLAY', false); // Turn forced display OFF
define('WP_DEBUG_LOG', true); // Turn logging to wp-content/debug.log
at the same time, comment out any lines that define WP_DEBUG as false. Then do a page reload and finally look at what is logged in wp-content/debug.log
that should at least give you an idea as to what is causing the 500 error.