I had an unusually hard time installing on my system (I hope). Around 4 steps below.

Here is a more complete description of everything I had to do to get FS to work on windows 7. 

Every file below was set to run as admin (R click on it or set it in properties).

What seems to have fixed it for me was:

1)  making sure (and  installing) the last known version of the 1.51 patch (2 GB version).

This at least allowed my computer to run 2142 on windows 7.

The earlier 2142 (smaller GB) versions of the 1.51 patch did not work for me at all.  When I installed FS they just constantly gave the "FirstStrike has stopped working" black screen error no matter what I did.

2) Even though 2142 was now working, it had red servers.  The solution was to re-install (again) 1.51 for 2142.

Of course it wouldnt let me re-install. It said something like "your patch is an earlier version" or something like that.

So I went into the registry (start then type REGEDIT) and set my 2142 version to 1.50.  Its under HK LOCAL MACHINE then SOFTWARE then Electronic Arts then EA GAMES.

Highlight Battlefield 2142, you should then see a list of details.  Its the last line you see and just says:

version         1.51

I double clicked on the word version and changed this to 1.50 

Thats all.  Just one digit change.

Now the latest  2 GB version 1.51 (2142) patch would install.

This fixed the red server problem for 2142 only.  I could play 2142 fine after installing the 2 GB 1.51 patch.

3) FS though still would not work (black screen and error on launch).

May be coincidence but the way I got it going on the windows 7 computer was to install FS completely before the launcher was installed - this is difficult as the launcher install window pops up before FS has fully completed installing.  (maybe just on my system - dont know).

  The FirstStrike install screen is totally different than the launcher install  screen. 2 different windows on the monitor at the same time. One under the other.

The FirstStrike window is small and is hidden beneath the launcher install screen and can't be seen (maybe only my 1920x*  widescreen resolution?). Since its under the other screen people ignore it and it doesnt finish fully installing FS.

The natural inclination is to do what the screen in front of you says (install the launcher before FS is finished).

So I moved aside the launcher pop up window doing nothing to it.

Saw the FS install screen underneath and clicked what it wanted (finish or something similar as I recall).

When FS was fully installed and done, I started to work with that launcher window which was the only thing left to install.

Again, not sure if this is coincidence but FS started working after this.

BTW: If you get it working and have red servers there is an easy fix:

4) Red Servers for FirstStrike:

I used Angel's fix and worked perfectly (in updates section):

went into 2142 folder and deleted the FirstStrike.exe

Copied the 2142.exe (which I knew functioned well for 2142 at least)
and renamed it FirstStrike.exe

then launched with FS launcher.

No more red server problem. Finally.

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EDIT: added some version changing details 10-30-11