Hi Betty%20annh75470038,
As you have mentioned you have moved all your Adobe CS3 suite programs on to your new Mac machine and now it prompts you to re-activate them. Follow the below steps to resolve the issue:
1- I would recommend you to first completely uninstall CS3 programs from your machine using the app uninstaller, after this run the CC cleaner tool to make sure nothing related to Adobe CS3 is left in the machine: Use the Creative Cloud Cleaner Tool to solve installation problems.
2- Now download and use the new serial number given on the following page to continue: Download Adobe Creative Suite 3 products.
If in case you face any trouble activating the software with the new installer and serial number then follow the steps in this link: Resolve "temporary activation expired" error for CS3 and Acrobat 8.
Let us know if this helps.