Since EA delisted Carbon and offers no digital purchase option, the community generally treats it as abandonware. Here's the safe path:

Go to MyAbandonware → search "Need for Speed Carbon" → grab the Collector's Edition (ISO) . It includes the 1.4 patch pre-applied and all DLC cars.

Use WinCDEmu or mount the ISO in Windows 10/11. Install normally. When asked for a CD key, the site provides one.