There is no way to determine the serial number of a PS2 if the owner does not know what it is. It wasn't on the registration card, and the CD is the same for every PS2 of that model. If you didn't write down the serial number, then there is no way for anyone to know which one was your daughter's PS2. You have to make a note of the serial number before the console is stolen.
I just so happen to be in this situation and also do not have my PS2 serial number, but I did register it with Sony (as well as all my other PS gear as they advertised on the PSN site).
Oddly enough, I can't find anywhere on the site where my gear is listed! Even though I gave Sony all of my info (which I expect them to have since I used their site to log them), am I SOL as well? If so, then there's no point in the registration!
Registration is for advertising mostly, not really for your benefit really. However if you talk to a live chat representative you might be able to get them to give you the number, as it will be in their system even though you cant see it. However its probably against the rules to give you that info but you can try, i dont know for sure.
What is the point of this thread???? Even if you knew the serial #, what in the hell could you do? It's not like the **bleep** things have GPS locators in them..... you can't track them..... >.<
Or do you know who stole it? In that case, I STILL don't know why you're wasting space with this thread..... lol