Unfortunately you don't have any change to install CS3 on an new computer. CS3 is dead. Even if you have an installer and valid serial number, the aged out activation servers were retired years ago. It's impossible to re-install CS3 now.
If you have an update of newer CS versions (like CS4, CS5 or CS6) you still had the chanceof using it. But unfortunately, that ship sailed long ago.
Your options are to change to the Elements versions Photoshop and Premiere or you buy a subscription of one of the Creative Cloud plans:
Creative Cloud Photography Plan -- approx $10/month x 12 months.
- Includes the very latest versions of these great products & services:
-- Photoshop CC and Photoshop on iPad
-- Lightroom on desktop, mobile and the web
-- Lightroom Classic
-- Portfolio website + hosting
-- Spark with premium features
-- Bridge
-- 20 GB cloud storage (upgradable to 1 TB).
Creative Cloud All Apps (31 + apps & services) or Single Apps Plans
https://www.adobe.com/creativecloud/plans.html
My System: Intel i7-8700K - 64GB RAM - NVidia Geforce RTX 3060 - Windows 11 Pro 26H2 -- LR-Classic 15 - Photoshop 27 - Nik Collection 9 - PureRAW 6 - Topaz Photo AI