Registration Code is Invalid

I bought The Sims 3 on my PC back in 2010. It was a download from Origin. I registered it through Origin because I bought the game legally. In 2012 my computer crashed and I thought it was time to upgrade. I got a new computer and downloaded Origin to try to download the game The Sims 3 again at no extra cost because I had bought it before. I downloaded Origin and logged into my account. It showed in the "My Games" tab that I had bought the game and it is still registered. I got the product code again and went to the Sims 3 website and recovered my password and went to the my account section. It said I have no registered game so I clicked register a game. I entered my product code from Origin over and over for about a month now but it still says "The serial code you entered is invalid. Please enter a valid serial code and re-submit." I want to download some things from the exchange but I can't because of this! Please help me!

PS: I do not have my hard drive from my old computer. It is wiped clean.