I see this post has been unanswered for a while bit I just came across the same situation and managed to fix it. I hope this may help you or further X-Com players with the same issue:
I re-installed TFTD (CE Edition) this weekend (this is not the first time that this has happened) and applied all the necessary patches (...but this is another topic). Howewer it was still crashing right after the intro.
Since I had already seen this problem before (due to a prior X-Com relapse on another computer) I assumed I had missed something with the patches).
So I tried another crazy thing by switching my langage option to english in-game (since I am french it wasn't my natural choice - nevermind, it's probably better worded in O.V.) and then reached the main menu and even got proposed to pick a location for my first base!
But then I got that issue you depict. I have actually changed two things so I can't tell which one made the difference (poor experiment design, I agree), still my likes go to the latter:
-I have connected a bluetooth mouse my laptop (Dell Vostro 1510 / Intel Core 2 Duo T83000 2.40Ghz, 3Go RAM / XP Pro SP3) because (1) I 'd rather use the mouse indeed but also (2) wondered if the trackpad wasn't creating some sort of conflict (but I don't know what I am talking about ^^)
-I changed the regional settings to english (and windows had me reinstall some files from the CD) because I figured there might be something about the way charachters are coded (don't know much about that either).
So for now it seems to work (haven't tried to manage the base(s) or the tactical phase yet) with a qwerty keyboard (most of you can picture themselves with an azerty one and many subtle but potentially nasty swaps).
I don't know if that will help, I hope so, you may find your way around within the above lines.
P.S: Sorry for the blah blah and the not-so-precise solution I suggest but now I have an alien invasion to contain!