Well, I installed the Demo, and when I try to enter the campaign, the loading screen comes up and 1 pip turns white while the rest of the loading bar stays dark and a message saying "Attempt to load the mission failed."
I switched the FSO build to "mod default" but that didn't fix the problem. It was set for 19 RC3 even though RC3 is NOT in the listed options (don't ask me how that happened). I switched it to 3.8.0 and that seems to have fixed it...
EDIT:...for about 23 seconds. Just started the first mission in the demo, approached the Shivan fighters and was about to fire when the game crashed.
EDIT2: Just tried it again and it crashed at the very same time, 25 seconds in.
I'm gonna try to get a log of this now.