Sims 3 code already redeemed

Okay, I know this is just another 'already registered' code post. But I can't find any help on the forums and I don't understand. 

YEARS ago, I bought the Sims 3 starter pack DISC VERSIONS with Late Night and High-End Loft. I installed it onto my mac with a disc adapter. I'd used the code - it installed but kept crashing, so I took it off and put it in my closet and that was that. 

NOW, I'm trying to play again on a Windows 10 computer. I was told the discs would not transfer (since discs are rendered pointless these days -.-). So, I downloaded Origin. I'm using the same codes from my discs since I figured, well, I already bought it. I shouldn't have to buy it again. It's saying the codes are already registered. Every forum I see tells me to log into my old version of Origin, I don't HAVE one. I'd used the codes via the discs - not downloading online. 

Please help. I'm not going to buy this game AGAIN. I will likely buy more expansion packs if it works but I'm not going to buy something I already paid for. This just doesn't make sense to me. If I uninstall a Sims game, am I just...NEVER going to be able to play it again?? How is this efficient? I don't understand; I've never had these problems with Sims 1 or 2.