If you're playing multiplayer, the AI log shouldn't matter since it wasn't creating during that game, since there are no AIs in multiplayer games at present.
Is the system you're trying to play on connected to the internet, and is there a firewall installed? There might be some incompatibility between FreeOrion attempting to communicate between server and client...
Edit: I'm actually on IRC right now with someone who was trying to play multiplayer and was getting crashes, and who was apparently able to fix them by adjusting firewall settings. It might help to run in windowed mode at first, so that if there are any popups from the firewall about freeorion trying to access the network, you'll be able to see them. /Edit
And can I infer from you previous posts that you're able to play several turns of a single player game without any crashes? The log files seem to end after some graphics-related debug messages, suggesting a graphics-related crash, but if you're able to play in single player, that's probably not the case.
I can't really tell what the problem is from the log files, though, so I'm not sure what else to suggest. You're not having the obvious and most commonly reported problems... It might be another language-related incompatibility, but I can't be sure.
It might help if you could build the latest version, or try one of the Recent Windows Builds
posted by pd, but that's really just a guess and hope...