Re: problems in NFS Carbon
The cd-key is stored in your save file. Patching to 1.4 should not have changed the savefile. If you didn't save your cd-key elsewhere, it should be stored at offset hex 3C in your savefile if you have a hex editor. There is a savegame editor which also shows the cd-key, but I don't know where to get it these days.
If you registered the game before EA shutdown access to the old (pre 2008) EA account system, EA tech support may be able to get the cd-key for your registered game.