Alright, to save yourself a lot of hassle in downloading the game, especially if you have a 384k connection, go about as follows if you can borrow a disc from someone.
1) In Steam, activate the game by using the cdkey you won.
2) Let the game start downloading via Steam, so that you can see it's busy in the Download monitor window in Steam itself.
3) Now exit Steam, then, take your DVD and initiate the install procedure.
4) Instead of installing it to another directory, install it directly to your Steam directory. Steam would create a folder for the game, for example:
C:\Games\Steam\steamapps\common\dirt 3.
Just verify if it's dirt3 or dirt 3 (with a space inbetween the dirt and the 3) before starting the installation procedure to make sure you install it into the right directory that Steam created.
5) After the installation has finished, simply restart Steam.
6) It will appear as if the game is still downloading, but have a look at the completion counter, it will go quickly instead
7) The only thing that will download extra, is that 600mb update they released for it not too long ago, but downloading 600mb is better than 8GB plus
8) ???????
9) Profit !
And that's basically it. Just wait for it then to download that update, but using this procedure will save you a lot of time and hassles, if you don't want to download it.
If anyone has any questions, please feel free to ask.