I wonder if the startup applette is having issues. When you ran directly from "C:\....totalgaming\galciv2", did you run the GalCiv2.exe file or GC2Loader.exe? (silly question im sure, but jsut making sure)
Also, check your root directory and make sure eveything was installed correctly. IIRC, the total game size was around 900 megs to 1.2 gigs, so if it's substanially less than that, perhaps something got screwed up with the install.
The game shouldn't be trying to go online. It'll only do that once you've gotten into the game and initiate a "metaverse" game.
Check your display settings and make sure it's displaying at 32bit color, just to be safe.
But the not creating a debug.err simply has me stumped