If the PHPList config settings look good, I would try something a little quicker than figuring out the whole shebang.
Create the DB (AND USER) on the Linux box.
Adjust the connection settings in the config file.
Run the install and see if it initializes properly.
If not… problem with nux config for PHP or MySql.
If it goes well…
Migrate the DB to the Windows server and adjust the config file to point to the right place.