Hmm, that's weird. First time we met with something like that. Did you tried to contact wpml support team? Maybe the problem is related with plugin's corrupted files? In the past we met few times with situations when weird things were happening when wpml was active but in each case, the problem was related with plugin's files.
Comments
all details about creating sidebars for pages, you can find on http://forum.muffingroup.com/betheme/discussion/10/how-to-create-sidebar-and-set-up-for-page but please remember that to set sidebar for categories or single post pages, you need to create blog page because this page is strongly connected with all posts related pages.
What about setting up posts page under Settings > Reading section? What exactly does not work?