While combing the search engines some months back, i discovered Skidrowgames where detailed instructions were given on how to go about the installation of the cracked version of Mass Effect 3 and it worked perfectly. So, incase you have similar issue -- here's the solution that worked for me.
1. Install the game
2. Copy the cracked content located in the \Crack directory on either disc into \Binaries\Win32\ of your installation directory, overwriting existing files. (This is the major part else the game will keep telling you that you need to install origin on your computer before you can play the game)
3. Launch the game and you should be able to play the game now
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