Sims 3 Serial Code

Hi, I don't know if someone else has had the same issue before, but i really need help. My friend recently gifted me the Sims 3 on Steam and I got a CD Key. I used that code to download the game on my EA App, it worked. But the Sims 3 website still says that I don't have a game linked with my account, whenever I try to register my game using the same code, it doesn't work, saying the the code is invalid.

I already contacted EA Help, but they said that it was a Steam issue, but when I went to the Steam Help site, it said to contact the retailer and I don't want to do a game of going in the circle of EA just saying that it is a Steam issue, when I don't think it is.

Does anyone have any way that they could help me to get this to work?

I really want to be able to download some of the stuff from the Exchange because it looks really cool, especially builds since I don't like to build at all.