yes but if you have registered it you can go on the website (forgot which one) and go to your account and check there and it shows your cd keys for all the ea games you have registered. it happened to me a few months ago and i actually ended up buying 2142 again but after i bought it i figured out something i missed before. i was using a different account that what i had my cd key registered on and boy i was frustrated with myself i felt really stupid that i had not realized that.
I did exactly the same thing a couple of weeks ago. Have you used EA Link to update the game or download the booster pack? If so it'll have your cd key saved in the account section.
I do have Northern Strike I got on EA Link... but would that have my CD Key for my game?!??!? I did not register unfortunately but I am registering every game from now on hahaha. Please tell me if having the Booster pack on EA Link will help and if so how to do it.
I think that in cases like this EA will give you a new one if you send them some proof of owning the game. It might take half a year, but just contact EA tech and see if they'll do anything for you.