I think that UAC was the cause of the problem, which I have now disabled. I will post my results after the next re-installation.
Results: I am at my wit's end. Nothing seems to solve this. My install directory is apparently missing a large amount of files (e.g. my data folder only has "maps" in it), but I have UAC disabled, and even my C:\Users\Username\AppData\Local\VirtualStore\Program Files has nothing in it. This returns me to my original theory: something is wrong with my network connection to the GOG servers. I would hope it is simpler, though.
Help, at this point, is very much needed.
Update: Actually, I think it was the "Mega MOD" recommended in the sticky that was doing this to my game. Seems like my problems are gone. Consider this topic my official thumbs down for the mega mod (for what that's worth).