Your copy of CS3 must be an upgrade from an earlier version, so now you need to provide both the serial number for CS3 and the old one you used to upgrade to CS3.
If you had registered BOTH versions, you can retrieve the s/n from your Adobe account.
Just a clarification in general:
Remember, you are not addressing Adobe here in the user forums. You are requesting help from volunteers users just like you who give their time free of charge. No one has any obligation to answer your questions.
Somewhere on Adobe, I believe, there is a program to remove the serial number. It is supposed to do a clean uninstall, even if you have already removed it.Your CS3 disk sounds like it is an upgrade disk instead of the full version though, so fully uninstalling CC probably will not help you. You will need to hunt down one of your older versions if that is the case. It will SAY Upgrade or something to that effect on the disk if that is the case, because that is how an upgrade works.
However, I am surprised you did not find CC better than CS3. The AUTOSAVE option, is well worth the switch, even if you do not count the smart fill options, and other new options.