Moved from Command & Conquer to SimCity.
On the subject of your question... in these days where piracy is abundant and you can more or less find the actual DVD images of games in seconds by searching online, that serial code is your only real proof of game ownership. It's really that simple. You lose your code, you lost your game.
If you're lucky you can get a new code by going to help.ea.com and clicking on until you get a live chat, and somehow proving to them you own the game (I dunno, by providing a photo of your disc or something), but I wouldn't get my hopes up.
You can always just buy it again - it's only $10 on Origin. And since that's on Origin and will be tied to your account, you can't lose it.