I also have the white map problem and my computer runs under windows xp - I have not had problems with any previous game - Victoria 2 runs fine - divine wind is ok - I have preordered sengoku - am I stuck?
Check if your graphics card has support for shader model 3, which Sengoku uses. If not, I think that can be the cause of the problem.
We are currently working on light-weight shaders for Sengoku which only requires shader model 2, my estimate is that we'll be finished with them on Monday. It'll just be a couple of files, so you can copy them to your demo directory and see if they solve the problem for you.