The "Product activation" button in the main menu is only used for multiplayer key activation and has no effect on the single-player portion of the game (it will not run in demo mode).
To receive a multiplayer key, please send a message to our Support staff here. After you receive the key, open Earth 2160's Start Menu folder, go into the Tools subfolder and launch the "Change Serial Number" application. Input the key here and press OK. Now you should use the "Product activation" function in-game, after which you will be able to play multiplayer games.