I took some screenshots of my game with the resource monitor on while in windowed mode. 

Here it is while at the menu screen.

When I loaded up my saved game.  It had already been at turn 197.  At this point I just kept clicking on the turn button, and expanding my cities, and the by the time i hit turn 291, the game was a little bit unresponsive at this point, and it did hang at one point for about a minute.  Also, there were weird instances where a couple of battles would not take place where they were supposed to be originally.  If you look at my save game (which I'll be providing a link to), there's a patch on the map that's uncovered even though I had not moved any units there.  For some reason, a battle taking place in one of my cities all of a sudden was transported to that patch of land.  It happened on two occassions. 

At the time I got my error message at turn 300 (Yes, I lost):

And finally a snapshot from the resource monitor:

Here's a copy of my debug:

http://rapidshare.com/files/410231745/debug.err.html

and a copy of my savegame:

http://rapidshare.com/files/410231841/oddgame3.EleSav.html

I'll try running the game with no audio to see if that does anything.