Given the difficulties in activation and OS compatibility, it is often more productive to look at modern alternatives:
If you have purchased the software and need your legitimate serial number, it is not too late to locate it if you registered it with Adobe.
If you own a legitimate copy of Adobe Premiere Pro CS3, the serial number would have been included with the original purchase—on a card inside the box or in a confirmation email from Adobe. Since CS3 is very old (released in 2007), Adobe no longer supports it, and they generally recommend upgrading to a current version like Premiere Pro (part of Creative Cloud).