Mine always asks for a password and I just type in "000000".
With the factory settings you can enter any # you want, unless someone has set a password.
If someone did set a password, try removing the disc and turn on the PS2. It should take you to the main menu. You might be able to restore factory settings from there.
when it asks for a password, type 0744, that will delete the pw, and put a new one in that you will remember, then go to the menu, hit stop twice, then go to the settigns menu, and turn off the parental controls ( or set them as hhigh as you want to). that should take care of all your problems