if you purchased and download cs3 from adobe or registered with adobe, you can find your serial number under the purchasers/registerers account, https://www.adobe.com/account.html
but you need to check the account used when purchasing/downloading and registering. ie, unless you were the purchaser or registerer, it won't be under your account.
you can contact adobe here to see if they can give more help, http://helpx.adobe.com/x-productkb/global/service1.html