Hmm... I downloaded the game from Abandonia, too, but I rarely have any problems (I run it with DOS-Box).
The only two problems I ever had:
1) I start a mission and suddenly the game decides to ask for the cd-rom
Solution: Restart DOS-Box and try again
2) The game freezes, DOS-Box starts mass-producing some errormessages in the 2nd DOS-Box window (the one with the cycles and everything)
Solution: Quite surprisingly, restart DOS-Box and try again :angel:
Anyway, I suspect you tried that anyway ... I never had any other problems with the game (at least none of technical nature

).
I don't know how you run the game, if you don't use it already, try to use DOS-Box
Otherwise, make a backup copy of your savegames and unzip the X-Com apocalypse archive again to make sure everything is there and in one piece.
I hope this sorts your problem out... and don't kill the messenger, even if he has problems with shutting up and just keeps on talking...
talking...
talking