Adobe officially retired the activation servers for Creative Suite 3 (CS3) in 2017. This means that even if you have a valid, original serial number, the software can no longer "call home" to verify it, which often results in activation errors during a fresh install.
Reactivate CS3 on new computer [CS3 is dead] - Adobe Community Adobe Illustrator Cs3 Serial Number UPD
Adobe Illustrator CS3, released in 2007, remains fondly remembered by many designers for its stability, speed, and iconic interface. However, searching for an “Adobe Illustrator CS3 serial number UPD” often indicates that users either lost their original license key or are trying to activate old software without proper authorization. Adobe officially retired the activation servers for Creative