thanks for the information so far.
I have now tried Episodes 3 and 6 as well:
With Episode 3, I can't even get beyond the intro. After the "car" scene is over and the title of the Episode is being displayed, the game crashes in one of the three ways I described above.
Episode 6 seems to work so far. I can start a new game or load an old one, no matter if there are save games present or not. I don't really want to play Episode 6 before I've finished Episodes 2-5, though.
Windows 2000 is not a supported operating system and I'm wondering if that has anything to do wtih this problem.
It does say "Win2000/XP" below the entries for Episodes 1-3 on the Downloads page.
Oddly enough, Win2000 isn't mentioned for Eps. 4-6, but still, Episode 6 doesn't seem to crash the way Eps. 2 and 3 do on my Win2K machine.