MySQL Connect Error on Development but not on Production Machine

OK. On to my next idiot's mistake.

I am getting the underneath error when connecting to my database from my home-based Development machine. Yet the exact same connection file, to the exact same database, using the exact same credentials, works OK upon the Production Machine located on my host's server.

Warning: mysql_pconnect() [function.mysql-pconnect]: OK packet 6 bytes shorter than expected in ... on line 9

Warning: mysql_pconnect() [function.mysql-pconnect]: mysqlnd cannot connect to MySQL 4.1+ using old authentication in ... on line 9

Fatal error: mysqlnd cannot connect to MySQL 4.1+ using old authentication in ... on line 9

The contents of the Connection.php script are a standard WebAssist file as follows:
$hostname_... = "www.xxxxx.com";
$database_yyyy = "yyyyy";
$username_yyyy = "zzzzzz";
$password_yyyyy = "youmustbekidding";
$sacredthread = mysql_pconnect($hostname_...., $username_sacredthread, $password_sacredthread) or trigger_error(mysql_error(),E_USER_ERROR);

That last line is the aforementioned Line 9.

I have already Googled the error. It's usually associated with a change in password procedures. However, I thought it might be best to figure out why this Fatal Error is happening ONLY when I run my file from my Production Machine (to connect to the specific database), yet the exact same credentials in the exact same file work OK when the file is located on the Server hosted by my ISP. I do not want to get my ISP to change any settings if it can be avoided.

I am sure this is simple. Most likely some setting in php.ini?

I have approached the wise here who I am sure know and have a simple remedy. Thanks.
Bye now.