First, deactivate the CS3 install on your "old Dell laptop". You'll have to call Adobe customer support to do that for you if you cannot connect that laptop to the web.
Once deactivated, you install CS3 on the new computer from your original CS3 install media (CD or DVD) or a fresh CS3 download from the Adobe site if still available.
Then apply all Photoshop and ACR updates manually one by one. I doubt the Adobe auto updater will work reliable with CS3.