The compagny behind mysql have changed some things to the way MySQL stores passwords in version 4.1. Because of this, php4 will not be able to connect to MySQL 4.1. by default. Below is a way to get it working:

Run through the MySQL installation. After installation is succesfull and you've run through the configuration wizard, open the my.cnf file that is in the directory you've installed mysql. 

Add the following line at the bottom of the file:

old_passwords

This will force mysql to use passwords old style. 

Restart mysql (or your pc, that will do the same) to get it working.

After this, you will have to change the allready stored passwords to be able to connect. Open the mysql command line tool to do this:

Start -> Run -> cmd.exe

Press enter to open the command line

Then enter:

cd C:\Program Files\MySQL\MySQL Server 4.1/bin/

and press enter to go to the right directory.

Type:

mysql -u root -p

and press enter, the command line tool will ask for your root password.

After this, enter the following command:

SET PASSWORD FOR root@localhost = OLD_PASSWORD('mypassword');

Where mypassword, will be the password you want to use. Press enter to set the password. After this you should be able to connect through php.