@Domitaino - I think you're supposed to have a digital key, too. There is a small help article on Steam on how to retrieve it - they say to verify the game cache files if you're not getting the choice to "View Game CD" : https://support.steampowered.com/kb_article.php?ref=2037-QEUH-3335
Just had another thought - Do you have to run Origin when playing from Steam? If you do, it may already be registered to your Origin account. Have you tried installing Origin without Steam and logging into your EA account. It may already be registered to your account.
If you can't run it in Origin, I'm not sure - you might have to contact Steam support to get the key? I don't think there's any way that EA Help would be able to cross-reference it. Please reply back & let us know how this goes.