I have the same symptoms, since going to Beta 2 [.50].
I also have lots and lots of hangs (need the task manager to kill the game). No dump files, either made by the game or by windows, are generated. I have tried playing a small map, but after 78 turns and more than 100 hangs i finally gave up.
During the previous Beta the game was rock-stable on my machine, except for identifiable bugs (and crashes). So the only time i now spend on the 'game' is not playing it, but going through the xml-files or trying to figure out the various underlying formulas.
I will wait for Beta 2 patch 1 and see if there is then an improvement. There have been a number of postings stating hangs, even on the most elementary things; like double clicking a planet, launching a ship, scrolling the main map, etc.
Like you said support can't do anything with this because there are no log/debug/dump files generated. However you can create a ticket, and attached the zip output from the support tool.