You have spaces in your constants, "MY DB TABLE NAME", etc (without quotes)
$this->connection = mysql_connect(MY DB SERVER,MY DB USERNAME,MY DB PASSWORD) or die(mysql_error());
mysql_select_db(MY DB TABLE NAME, $this->connection) or die(mysql_error());
As I recommended before, re-download the database.php from the site you got th elibraries from, and use the original.
When using constants, they have to be entered EXACTLY as are found in the constants.php file.. if they have underscores, use underscores.
In PHP, constants, as identified by define(), can not contain spaces or other reserved/illegal characters in PHP, similary to variables or function names.
Make sure that the "MY DB SERVER" is entered EXACTLY as in constants.php, if it's "MY_DB_SERVER" then it must be exact (without quotes).
And as mentioned before, it helps us to diagnose issues if you leave ALL programming code between the bbcode tags php and /php, entered like
[ php]
and
[ /php]
You will notice that i have a space between the [ and the php (or /php) that is only to show you how to use it.
If the above (bbcode tags) were correctly set without the space, you would see something like:
and
best of luck with the constants file.