It works perfectly for me on my mySQL/PHP/Apache web server.
First thing to check is your username and password, as well as your domain name.
Make sure all are EXACTLY correct.
It almost looks like your screenshot is showing a syntax error on the page, not a mysql error.
What I would do is to copy-and-paste the EXACT info you posted, and create a new .php file named something like 'test.php' (without the quotes)
Then, just open up IE/Mozilla/Netscape/Opera and shoot to that page.
HTH,
David