Here's another fix for you to try:
Download http://sd.stardock.com/gc2_metaverse_remove.zip and extract that to the Twilight directory.
Then remove \ProgramData\stardock\gc2ul\sig.bin
You will need to reactivate but it should work properly after that.
Today I got an email from Stardock support that confirmed that if I didn't have a gc2ul folder, but that I did have a sig.bin in ProgramData\Stardock\Twilight, I should delete that one and follow the rest of the instructions in Rosco_P's post above.
So I removed that sig.bin, downloaded the zip file, extracted it into the Program Files (x86)\Stardock Games\GalCiv2\Twilight directory, replacing the files already there, and started GC2 TA. I had to re-enter the registration information, and then the game let me into the metaverse, select my character, and start the game with no crashes.
So, success at last for me. I hope the same solution works for some of the rest of you having the problem.