How to install NFS:ProStreet with key, but without disc?

Hello NFS-Community,

I'm having trouble with my installation of NFS:PS, because my disc is quite scratched and it seems it is not readable anymore.

I have still got the key for the game at the back of the manual, and so i was wondering whether there is any way of legally installing the game without the disc.

I've tried entering the game key in Origin, but it did not work. Is there any possibilty to download it somewhere?

Can you help? I really want to play this game.

Thanx to all of ya! Love ya!