Try this maybe:
May be coicidence 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.
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 posted in another thread.