How to install an already registered Sims 3 game?

I used to play The Sims 3 on my parent's computer but now I got a laptop. This laptop doesn't have a disk drive so I tried to register it into Origin. I put in the code then the window showed up to confirm that it's my game. It has my email, so I know that it s mine. Then I hit the next button, and it says that the code has already been used, which makes sense because I already registered it on my parent's computer, however I want to play it on my laptop. Is there any other way of installing my game? I'd be really disappointed if I have to buy another game. Thanks.