I had the Sims 3 game but I had to uninstall it as I had same issues with my computer. When I try to install it again it asks me for the registration code but I don't have any...
You can try going to your Sims site account and trying to locate it there. A product key finder might also help. Call customer support to see if they can further assist you.
When you were delivered that game, you must also be provided the key. If not, then you can go back to the site you bought, check the delivery and find the product key. Otherwise, consult a customer support member are make a ticket.
Go to the site from which you bought it and ask the seller who provided it to you. He will be able to help you in this kind of critical situation.