Well, I have good news for you. :-)
If you have the Origin client installed on your computer, you can use the "redeem code" option to enter the serial number for your game which will then cause it to appear in your My Games tab when the client is running. You can then click on it and tell the Origin client to download and install it and all related content and it will cheerfully do so. Problem solved. One of the very few things I actually LIKE about the Origin client. Once you use Redeem Code and the serial number from any physical copies of EA games you own, you can always download and install the digital copy of the game. Broken/lost/damaged disc? Not a problem any longer.