Can't connect to remote MySQL server using PHP

obviously I am doing something wrong when I try to connect to my db. Please help
the code I am using is something like this:

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1. <?php function connect_db() {
2.   global $link;
3.  
4. $host = 'server.root.com';  (Ps: Note I am not using www.server.root.com)
5. $user = 'username';
6. $pass = 'password';
7. $dbname = 'database'; 
8. $link = @mysql_connect($host, $username, $password)
9.     or die ("Could not connect to database");
10.  return $link; 
11. }
12.  
13. ?>
14.  
15. <?php if (!isset($link))
16.  
17. connect_db();
18.  
19. @mysql_select_db ($dbname)
20.     or die ("Could not select database"); 
21.  
22. .....
23. .....
24. ?>
25.  

I am getting a message saying "No Database Selected"

I have just started using mysql and php hence the high level of ignorance. I would appreciate help in any and all forms.

Thanks in advance

shawzozo