If you don't know the date of birth that you registered for the account, then you cannot reset the password online. Period. You will have to contact Playstation customer support by phone or live chat during business hours (https://support.us.playstation.com/app/contact_options). Whether or not they can help you depends on how accurate the rest of the information that you registered was, and how much of that you can remember.
you don't need to contact customer support, you need to contact your mother! Seriously, how the **bleep** do you forget your date of birth? you better write your name down in case you forget that next!
Obviously he lied about his age so that he could create a PSN master account, even though he wasn't old enough to do so legitimately. Then he wasn't wise enough to write down what date-of-birth that he used, or better yet use a parent's date-of-birth; so he could always find out what it is later. A lot of kids make that mistake.
I have lost my Playstation network ID password
You can try to log in here: https://account.sonyentertainmentnetwork.com/liquid/login.action
Click on "trouble signing in?"
** Engage brain before putting mouth in gear ** ** two-step verification - use it **
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