Just to be sure, you downloaded and installed the latest patch from Blizzard? You can do it directly from their website, you don't need to connect to Battle.Net.
I have been facing this problem, whenever I run War Craft 3 on my cousin PC (having Windows Vista), I get an error "Windows NT not supported". I have tried the following instructions:
But after trying, I still face the same issue. Any other suggestions for a solution to this problem?