A couple of points:

• I don't know if it's just a copy-and-paste issue, but you have too many colons in your $dsn. It should be

  $dsn = 'dbi:Sybase:My_sybase_server';
  [download]

• More importantly, do you have the Sybase client installed on your machine? Even if the server is located on the box, you'll need the Sybase Open Client to connect.

A good way to check would be to try using some other facility (some freeware client, for example) to connect to the database. If that fails or succeeds, it should give you a strong clue what to do.