I was wondering if can or should be able to connect to database from my local machine

Example my constants file
define("SERVER_NAME", "123.45.678.91");
define("USERNAME", "grpwrk1");
define("PASSWORD", "abc123");
define("DATABASE_NAME", "grpdb1");

This works fine from my http://www.mysite.com
Database connections and database selection works along with retriving data.

If i want to download the files and work on my comp with the same constants file work
Will localhost/htdocs/mysite.com still be able to work

So far i am getting this error
Warning: mysql_connect() [function.mysql-connect]: A connection attempt failed because the connected party did not properly respond after a period of time, or established connection failed because connected host has failed to respond. in D:\xampp\htdocs\tutorials\countrysideni.org\includes\db_connection.php on line 10
Database connection failed: A connection attempt failed because the connected party did not properly respond after a period of time, or established connection failed because connected host has failed to respond.

Is it because what I am trying to do will never ever work or do i need to change some settings?

Pierce