Unable to contact EA server to validate installation and play game

Regarding Battlefield 2142:

Despite its age, it is in concept and mechanics, an excellent game; and in my opinion, the best game ever created.

Your understanding regarding EA's Internet server service is correct. EA servers for the game have been discontinued.

However, it is still playable both offline and online.

Note that the game needs to create an offline profile before it can be played in singleplayer. However, that offline profile is only created if the game is first launched in multiplayer for a game on an Internet server. Given that EA servers have been discontinued, the typical alternative is to run the game on GameRanger (an online multiplayer service) that will create an offline profile for you.

So:
1) Download GameRanger from its website at www.gameranger.com;
2) Install and run it;
3) Create an account for yourself on it, which will include a GameRanger ID;
4) Locate a Battlefield 2142 game to play on GameRanger;
5) Click to join the game from within GameRanger;
6) Battlefield 2142 will run automatically and you will see a new profile appear in the game that uses your GameRanger ID.

This new Battlefield 2142 profile will also be your new offline profile and will allow you to play singleplayer. The method to play singleplayer is to:
1) Run the game independent of GameRanger (i.e. run the game by clicking its icon as usual);
2) Ensure your Internet connection is off, otherwise, the game will try to look for the EA server and take a lot of time before it lets you run the offline profile.

Also, did you ever run the game successfully before the EA online service shutdown? If so, I can add additional information that will help you run singleplayer more conveniently.