I realize this reply is about a year after you started discussing it...hope someone sees it someday.
I have managed to get Generations to run on my PC running Windows XP. I initially ran into the same trouble you mentioned regarding the game crashing as soon as you started an away mission, HOWEVER I have found a solution -- an absolutely ridiculous solution that you won't believe, but a solution nonetheless.
I know this sounds crazy, but stay with me on this...As soon as you click "Transport" and you hear Picard say "Commander Riker to the Transporter Room" begin RIGHT CLICKING YOUR MOUSE LIKE CRAZY. I don't know why, but as long as you do that the game won't crash and the Briefing Screen for the Away mission will appear (I believe you can acheive this by left clicking too, but I prefer Right clicking so as not to accidentally hit the "Proceed" button before having read the objectives). Make sure you remember to do this before every single away mission, and start doing it well before the actual loading begins (I do it as SOON as Picard starts speaking).
I'm curious if this solution works for anyone else...if it does, does anyone have any idea why? Something about keeping the game "busy" so it doesn't have time to crash??? No idea here.
I sure hope this helps you. One problem I have is that despite this solution, the game still refuses to play cutscenes...do they work for you? At least it's possible to watch them directly from the CD by opening the files with Media Player...
Haha, you might wonder how exactly I stumbled upon this fix. It was nothing more than pure frustration -- I began clicking wildly out of anger and it just happened to work. Ever seen the movie Back to the Future? Remember the scene near the end where Marty can't get the car to start so he just slams his head against the wheel and -- presto -- it starts? It was a lot like that...my reaction of complete disbelief was just like in the movie too.