Has anyone found a way to do this? Since everyone with the original game has 3.1c I can't join their games (and vice versa) since the GOG is only version 3.1.
Very frustrating.

The GoG version is already at 3.1c, or its equivalent.

See this post.

Hmmm I wonder why it continues to do this then.. maybe a windows issue?
Anyone else had trouble in games playing people with a non GoG version?

Are the people you're trying to play with using a mod? If they are, you will need to install the mod they are using, as far as I know.
Edit: Also the DirectPlay interaction for LAN play me be a bit broken depending on what you're using to play this. For instance, using any older DirectPlay enabled game in Wine on Linux has been pretty broken the last few times I've tried it, but that wasn't specifically Total Annihilation.